There is Turtle Cove, Salt Mills Plaza and Ports of Calls for some shopping, restaurants and bars. We did not rent a car and wished we would have. It would probably be a good idea since the Gecko Bus is no longer in service.

Most activities are water related. There is not much nightlife. We are very active on vacation and we did find the Island somewhat boring. Maybe in a few years after the construction is completed we might find it a more livey destination.

provo is my favorite island. it is small but not easy to get around without a car. plenty of rental agencies and taxis are easily available though. maybe rent for 2 days would be enough to look around. go out to chalk sound - its an amazing color and the villas out there are quite flashy. you might enjoy one of the snorkel tours or a trip to middle caicos to see the caves.
there is not a town center. as kvr mentioned there a bit of shopping but it is spread out over the island.
there are not late night clubs or discos.
provo is a beach lovers destination. it became known because of 11 mile long stunningly gorgeous grace bay beach. (turkoise is located on a very nice part of the beach!)
ppl started going for the diving and bonefishing. and it has become known as a snorkel destination as well. tiki hut is fun at happy hour. the bar at grace bay club is a must see.
personally i am horrified by all the over building and hope the nature of the island does not change in the future.
here's a map that might be helpful for you: http://www.aquamarinebeachhouses.com/map.htm

on the other hand if you have not already paid for this trip you might look at the ai's in the playa del carman area south of cancun. big ai's with tons of activities. also loads of stuff to do out of the resorts like zip lines, ruins, atv jungle tours, etc. shopping in playa is a hoot and it is endless. plenty of nightlife in town also. we had a great time staying just south of playa in a villa.

Been to Club Med T & C twice. Both times I was single. Other than leaving the resort to go diving, I don't think that I ever left. Be prepared for beach, partying, drinking, being hit on, playing fun but silly games you swore you never would around the pool, and whatever watersports you are interested in in-between (repeat as necessary each day). It's definitely fun for singles in their 30's but, if that's not who you are or you want lots of activities outside the resort, you might want to look somewhere else.