Now try this one: End-build with greatest Speed per turn (consistently, that is, so +10 move for first turn, etc. is not applicable).
Here's a quick and simple Level 20 build, ignoring magic items, outside spells, shapechanging, and flying speeds: (I don't have time to research shapechange forms, items, etc.)
Wood Elf: 35
Monk 6: +15
Wizard 5 (Bladesinger): +10 when Bladesong is active
Rogue 9 (Scout): +10 and Cunning Action
Mobile Feat: +10
Longstrider Spell: +10
Haste Spell: Doubled Speed
So after casting Longstrider and Haste on yourself, then activating Bladesong, your base speed is 180 feet when not wearing armor. With a Move, a Dash action, another Dash action from Haste, and a Dash Bonus Action from Cunning Action, that's 720 feet per round, for 1 minute at a time.
Even without any spells or Bladesong active, your base speed is 70 feet, and you can move up to 210 feet every round (Move/Dash/Bonus Dash).