I have recently travelled to Stone Town, Nungwi and Jambiani. If you do decide on Stone Town, the Clove Hotel would be good especially if you are on your own. It is very central and has a great roof terrace (I didn't stay there as it was full. I stayed at the Hotel Kiponda which I really liked, but it did not have a very 'communal' feel). My tip would be to take a small compass with you to help negotiate the small alleys (at least you will be going in the right direction).
We stayed at the Nungwi Inn (they have various rooms there). It is right on a beach that you can always swim at and very close to bars/restaurants etc. We visited Kendwa - which also looked good - but seemed to have more expensive accommodation than Nungwi. It is all very much 'on the beach'.
In Jambiani we stayed at the Shehe Bungalows (which are very cheap at $35 inc breakfast). They are in a fabulous location right on the beach but to be honest the rooms are very basic. Also - depending on when you are there you may or may not be able to swim (tide times vary every day - you may be lucky and have the sea by 1430, on other days the tide could go out at 0900 and not come back in until 1700 or so!)
Jambiani is a really nice village where you can mix with the locals a bit (there is a lot of activity on the beach - fishing, seaweed farming, kids playing, football etc plus a village with a few small shops). In Kendwa and Nungwi the tourists are quite separate from the locals.
Zanzibar is very beautiful and definitely worth visiting. Just bear in mind wherever you go that there are a lot of power cuts and the water often goes off as well.
Edited: 6:35 am, February 14, 2013