For the Core Rulebook alone, this is actually not to hard to figure out:
None of the core races has a base speed greater than 30ft. Human is a great choice for the bonus feat.
Being Human, we have 11 feats at 19th or 20th level. These are quite simple to assign: We'll put one of those into Run and the other 10 into Fleet, which explicitly stacks with itself, for a flat 50ft. untyped bonus to our land speed.
Among the 11 core classes, Barbarian (Fast Movement, land speed, untyped), Druid (Wild Shape, replaces base speed), Cleric (Travel Domain, all speeds untyped), and the Monk (Fast Movement, land speed, enhancement bonus) have class features for increasing their speed that are not spells.
Land speed is quite difficult to achieve, but note that land speed is not limited by any of the Beast Shape forms, thus requiring fewer druid levels. A 4th level druid can transform into a Deinonychus with 60 ft. base land speed.
It does get a little tricky with the Polymorph rules:
While under the effects of a polymorph spell, you lose [...] any [...] movement types possessed by your original form. You also lose any class features that depend upon form [...] The GM is the final arbiter [...]
But considering that an awakened deinonychus monk/barbarian would have both Fast Movements, I'll assume our Monk/Barbarian/Druid can keep both them in Wild Shape.
We don't need more than 1 level of Barbarian for Fast Movement, or more than one level of Cleric for Travel Domain. We'll put 12 levels in Monk, for a 40ft. enhancement bonus to speed (level 13 and 14 do not increase our speed). The last 2 levels can be put in druid to increase the duration of our wild shape from 4 to 12 hours.
Our Human Barbarian 1/Cleric 1/Druid 6/Monk 12 now has a land speed of 170 ft. in dinosaur form (12 hours a day), which is quintupled when using the Run action, for a total of 850 ft. of movement per round, which is 96 miles per hour.
Flying is actually easier: Let's look at transforming into an Air Elemental using the Elemental Body IV variant:
Air elemental: As elemental body I except that you gain a +4 size bonus to your Strength, +6 size bonus to your Dexterity, and a +4 natural armor bonus. You also gain fly 120 feet (perfect).
This is available at 12th, leaving us with 8 spare levels. Taking 2 levels of Barbarian, for the Swift Foot rage power, giving a 5ft. enhancement bonus to all speeds, and 1 level of Cleric for Travel Domain's 10 ft. bonus brings us to a total of 135 ft. while raging (130 otherwise), before feats.
Over all, our Cleric 1/Barbarian 2/Druid 12/X 5 ends up with a fly speed of 185 ft., quintupled when "running", for 925 ft. movement per round, which is about 105 miles per hour.