While it might be a little underwhelming to only be able to walk around Clock Town for the first cycle, these are some of the routes you could pursue in the meantime:
Rupees are the main currency of Termina so you will need a few for the rest of the game. You can choose to grind some rupees right now while you're stuck in Clock Town. Don't forget to hand over rupees to the bank, at 200 rupees in the bank you'll get an adult's wallet. The easiest way to grind I found was smashing the grass in North Clock Town over and over by leaving and entering the area.
Deku Scrub Playground
The Deku Scrub Playground is a way to make a few rupees and a heart piece. Since you have to go back 3 times in one cycle to get the heart piece, you might as well do it now you're locked in.
Buy a Bomb Bag
Post Office (First Day)
The postman might be able to give you a heart piece on the first day between 3PM and 12AM, that's if you're able to beat his minigame.
If you collect the first Title Deeds by exchanging the Moon's Tear, it's possible to get another heart piece at the Stock Pot Inn, every day from midnight till morning.