If I play a spell with targets that I hid, do I have to choose those targets from the battlefield I hid it at?

Yes. If a hidden spell or a play effect of a hidden permanent chooses any targets, those targets must be chosen from among options at that battlefield, unless the ability explicitly restricts targeting in a way that makes this impossible. (Weʼll talk more about this later for specific cards.)

Related: Rule 811.1.d.2