It actually does say you can choose if you move, several things about when you can choose to move, and lots of stuff about when you can’t move or how much it cost you to move, or to move in certain ways, but you’re correct that (unless you’re using the Variant: Playing on a Grid) the game rules never specifically say the character moving gets to choose where they move, only how far.

Of note; certain game effects, such as the frightened condition, or the effects of spells like dissonant whispers or confusion can limit, enhance or control certain aspects of a character’s movement that might need to be wordier if a specific blanket general rule explicitly said players can choose where to move.

Also of note; The example given in the rule for using the Ready action if “you choose to move up to your speed” (emphasis mine) is “If the goblin steps next to me, I move away.” This example implies that you do at least choose which direction, at least in general, you’re moving when you choose how much to move, even if you don’t get to choose exactly where to move to.

Another noteworthy rule; Becoming Lost under the Wilderness Survival section clearly indicates a circumstance where the characters do not decide where to move, but the do determine a desired direction and a successful ability check allows them to move in that direction.

Certain exceptions apply; for instance, some means of movement such as the spell dimension door do allow to choose exactly where to move, (certain restrictions apply,) or if a creature is an independent mount is “it moves and acts as it wishes.” (Being an exception based game certain rules may contradict that creature’s wishes, such as the rule that says you can move up to your speed on your turn.)