On your first visit you absolutely have to walk to the top of the Pilgrim Monument! And be sure to check out the Provincetown Museum at the bottom. If you are into art then go to PAAM (Provincetown Art Association and Museum).
You might take a whale watch tour. And Art's Dune Tours are a great way to get out and see the dunes. There is hiking and biking on Beech Forest Trail. The Province Lands Visitor's Center is interesting.
As for restaurants there is plenty of fresh seafood of course. My favorite restaurant is Victor's on Bradford Street Extension. It is tapas style and is and excellent way to try several different things. The Red Inn and the Mews are also great. Make a reservation for the Red Inn. Napi's is interesting and different. The Lobster Pot is a bit touristy, but as they say, it is a Provincetown institution.
You can also get light, informal meals at one of the small, take-out places in Lopes Square and then walk down MacMillian Pier and sit on a bench and eat as you look at the harbor.
Some useful websites for Provincetown: