Aarakocra in 5e have a flying speed of 50 feet. But there doesn't seem to have a whole lot of other specifications on flight.
How can I give characters challenges when many of them are avoided through flight? For instance:
An inescapable pit is made escapable with flight.
Scaling a tower or mountain is made simple by flying to the top.
How can I keep challenges like this without getting rid of their flight all together?
There are ways to prevent easy flight -- Strong Wind (DMG p.110) is the most obvious -- but maybe the more important response to your question is to ask:
Early-access flight isn't unique to aarakocra. Many spellcasters can cast Levitate at 3rd level and Fly by 5th, and Druids can wildshape into birds at 8th level -- and spider-climb, which can accomplish most of the same tasks, is available by 2nd or 3rd level for most spellcasters. A number of classes, races, or items can provide short-range teleportation at low levels, which brings up many of the same questions. If your story depends on the heroes being unable to access specific physical locations, you're going to have a lot more problems than one guy with wings.
But I think you'll find that it doesn't happen as often as you fear.
Unless the entire party can fly or teleport, they can't really bypass most situations by just flying over it. Okay, one guy got over the castle wall -- what now? Either he's alone in enemy territory and has to find the drawbridge controls, which is a nice little adventure beat of its own, or he throws a rope down and everyone else has to climb up, which is making rolls to accomplish a task (and not real different from the barbarian climbing the wall first, or the rogue throwing a grappling hook up). And if the party spends resources (spells, items, etc) to bypass a problem, then what's wrong with that? They're correctly using their characters' abilities to face challenges.
Some of your questions make me a little worried. What is an 'inescapable pit', exactly? Is it immune to being spider-climbed, misty-stepped, grappling-hooked, and so on? How? Do you really want that in your game? If you feel you need to continually put 'no return past this point' signs in front of your players, you might be railroading them too much. They should be moving forward because they want to finish the job, not because it's impossible to walk any other direction.
Sure, aarakocra can fly at will, but the rest of the party can't. It might be trivial for that arrakocra to get to the top of a castle via flight, but does that matter when they are leaving behind the four other members of their party? The aarakocra might be able to fly out of a 80 foot deep pit with smooth sides, but the half-orc fighter in his party who fell down it and broke both his legs can't.
Perhaps the aarakocra player begins to think he can carry everyone to victory, one at a time. Well, what about the creatures in the sky? What about rangers or wizards who are looking out at the top of the castle?
This is especially true if the enemies know they have an aarakocra in the party, and they have used flight in the past. Assuming they are capable and intelligent, they would begin to prepare for something like this. Rangers with experience hunting flying creatures. Wizards that can cast earthbind. Druids that can wildshape into a flying animal. Even something as simple as equipping the people at the top of the castle with throwing nets would negate the ability to fly.
You could even just use weather effects, if it isn't somewhere that is actively defended. Sure, the aarakocra could take to the skies, but with the incredibly strong thunderstorm going on, there's a high chance he could be blown off course or struck by lightning while in the air. Is that worth the risk? Probably not.
Point being, one party member being able to fly shouldn't negate everything. The other party members still need to deal with traps and enemies, and intelligent enemies will easily begin to make changes to their defenses in order to shut down one person with wings.
Do not try to get rid of flight as option. many spells, racial or class abilities can grant flying. If you start doing it you'll basically never be able to stop placing one restriction after another.
What you should look into is what type of hazards, enemies there might be in the skies above? What kind of monsters, enemies might notice a single flying character or a group of them?
The situation is just the same as with swimming, players might avoid a guardpost on a bridge if they swim across a river but the river might be home to alligators or piranhas.
The skies are full of life, in D&D even more than our reality, including magical beings (worst case dragons), perhaps floating castles with an annoyed wizard not liking outsiders to come too close (the 'get off my lawn!' reaction).
Then there is also weather. Druidcraft can help players to avoid bad things.
If your players prepare for flying with care be sure not to punish, perhaps even reward them. Example: They cast invisibility on themselves. They might avoid an encounter and maybe even spot an enemy group, which they can now while flying eavesdrop on.
You could:
In the end, you could of course just disallow using Aarakocra or similar races. Adventurer's League does so (or did, I'm not 100% sure). Obviously, this won't work if the campaign has already started.
Also note that, at level 5, your magic users will be able to choose Fly as a spell. Therefore they might always have it available as a problem-solving mechanism as long as they want to use spell slots on it. See also this question on why flight is mostly unavailable at lower levels. It's about Pathfinder, but the principles are largely the same.
Very important: don't over-punish your players for being creative and using their abilities!
This will likely disappoint your players and take the fun away from them. Give them the occasional chance to benefit from their flight, either in a fight or to help out with an otherwise dire situation.
Always remember: The players are the heroes in the story told in a D&D campaign - not your plot.
Other answers have great suggestions for how to give non-combat challenges to Aarakocra players. However, many Aarakocra players use a tactic in combat where they'll fly just at the edge of a weapon's range limit. They'll fly into range, shoot their weapon, and fly back out of range. This is obviously limited to certain conditions, but in an open terrain fight without proper counters, this can remove any sense for danger for that player and unbalance fights.
The simplest method is to have a few enemies with ranged weapons that take the Ready action on each turn. They would ready the Attack action, with the trigger being "when the Aarakocra flies within range". This does consume their reaction as well, but I find that my players usually don't risk opportunity attacks, so my NPCs rarely get a reaction anyways. This allows your ranged enemies to shoot the Aarakocra player as effectively as the player can shoot them. You should use this tactic frequently
One single arrow, empowered by Ensnaring Strike, can send a flying creature hurtling to the ground. If they've been hovering just out of longbow range, they're going to be 150+ feet in the air - that's 15d6 fall damage. Similar effects that restrain, incapacitate, or inflict the prone condition can drop flying creatures out of the air, inflicting very heavy damage.
One word of caution on this: don't give every group of enemies someone with spells that can knock them out of the sky. Don't even give most of your groups that ability. Doing so will essentially be ruining the player's fun. It would be on a similar level to constantly taking the Wizard's spellbook. If they can do a cool thing, let them do the cool thing, but don't let them do it freely and without consequence. It will only take one or two instances of your Aarokocra plummeting out of the sky, magically fast asleep or restrained by vines, before they rethink whether they want to fly that high.
Aarakocra players who spend every fight hovering just out of range tend to feel that they're safe just because they're in the sky. It's your job to disabuse them of this notion. Occasionally have the player encounter an enemy with a fly speed that would be a good challenge for the whole group, and have the enemy go after the flying player.
At this point, your player will realize that what they've done is to isolate themselves far from the rest of their party, out of range of most spells and in a location the rest of the party can't reach. A territorial griffon wouldn't be very hard for a low-level party to handle, but could be absolutely terrifying for a lone Aarokocra. That could turn into a very interesting fight as they desperately try to descend to their party's reach while being grappled by the Griffon and provoking opportunity attacks.
Something else to keep in mind Aarakocra is a "up to" 5' tall BIRD humanoid based on the Eagle or Macaw (See Aarakocra Desc in XGE)
Based upon this, and the wingspan to body height ratio of those birds... An Aarakocra, on average, is going to have a wingspan of at least 12-15 feet, possibly as much as 15-20 feet. Those birds wings are each 1.5-2x the length of their body. So to fully extend their wings they need, bare minimum... 12 feet or so, more likely somewhere around 17-20 if they make the mistake of being 5' tall.
So... in a 10' wide hole he isn't flying anywhere because there's just not enough room for him to get enough lift to fly. Same for any other enclosed spaces. They'd have a tough time flying around in a dense forest, for example, or a cave system that doesn't have a lot of open space.
Don't restrict flying just because a player is a race that can fly. There are PLENTY of other ways to fly in D&D that you're going to have to deal with as a DM eventually.
Flight does solve some problems, and that's OK. It should.
Ranged weapons and magic spells are your friends. Even goblins and skeletons can use shortbows. Ranged spells can be pointed up, including such spells as Web, which, while without anchors would collapse once cast, still should gum up a flying creature and cause it to fall out of the sky.
Also, you as the DM can pay attention to the rules about minimum flight speeds and which flying creatures can hover (aarakocra not being among them). Also, having enough room to spread the wings and fly, to take off and land, etc.
In my world, I have also instituted a houserule, drawn from older editions of D&D, that a creature that flies using wings (as opposed to magic) loses its ability to fly, and must make a controlled landing, once it is below 1/2 its hp. This actually benefits the party more than it hampers them, but I think it makes for more interesting combat and tactics in fights involving flying creatures.
