If he wants to be able to see you for the whole of your stay then he should be paying your 24hr (or whatever) rate, not 6hrs. I
would just not answer the phone until the time of your booking with him, and don't give him the room number until an hour before your booking. if he queries where you were, just say you went sightseeing, or you were in the gym, or just watching TV.
he has chosen to pay for 2 nights but only 6 hours of your company. If he wants more then he has to pay. Its irrelevant where . you are or if he's paid for the room and travel. (Assuming it's not a sugar daddy arrangement?)