One trick to making things feel epic is to highlight the history of the place as they travel. This is pretty much one of the big things Tolkien loved to do - he'd talk about some mountains, what they were named, what they were named before that, who lived there, who lived there before that, which ancient spirit shaped them, etc.
Of course, this kind of thing either excites players who love lore, and bores everyone else. I usually like to give some recent history (within a generation) or "folklore history" that, in a fantasy world, you're not entirely sure if it's literal or just a story. ("That's the Demon's Chasm. Long ago an angel threw down a demon and it gashed open the land. Now it's just great fishing in the river at the bottom.")
It can also tie to recent politics - if you point to abandoned villages from a few generations back, or a town that's half covered in a landslide, it can be interesting when the players encounter NPCs who have history from those places. "This town changed two generations ago when the refugees moved in. The mountain nearly fell on their home, so it's not like they could go back, but the old families really didn't like them coming in..."
Aim the history towards player characters who would mostly likely know it - make it a reward for history skills, or being elves, or druids, or whatever would mostly appropriately fit.
The People that you meet
Tying in with the history idea of the places, you can have NPCs comment when they find out about the journey. "Wait, you're going to travel all there way THERE? Just the five of you?!?".
Have characters ask about faraway places. Ask if rumors are true ("Do they REALLY all have wings and fly from mountains?") Have shopkeepers willing to buy relatively mundane things at a good price ("Is that rope woven from North Mountain vinery? I'll pay triple! We haven't seen that in years!").
If the journey is long and unusual, the players might go through it relatively quickly, but the NPCs will definitely comment on it.
Like anything in a tabletop rpg, the question is whether something produces fun choices or not. A lot of sandbox style rpgs use maps, because maps create a set of choices - where to go, how to get there, etc. That's one way to make travel more interesting.
There's always room for things like combat, or hazards - a blizzard, a crumbling bridge, etc. The trick to anything you add is to make it about hard choices - do you take the short, dangerous route, or the longer, safer route. Do you lose important supplies and get away safe, or do you try to get them even though you're being pursued? Do you go back and free the guide who got captured or do you leave them to their fate because in 2 days the snow will block the pass?
One of my favorite RPGs, Mouse Guard, makes every journey feel pretty epic because the challenges you face are difficult. On the other hand, there's not really any MMORPGs that do stuff like this, and players either find themselves going "Wow, I have to apply creativity to survive in brutal nature! Awesome!" or they go "Guh, this weather sucks. I feel like I'm being punished just to play." Knowing what your players want is critical to making travel work.