I can see Block Island from my living room, but I've never spent the night :)
The Hotel Manisses is supposed to be nice, as is the Springhouse Hotel.
I wouldn't stay at Ballard's. The only reason to go to Ballard's is to drink on the beach :)
I've heard good things about the Blue Dory Inn.
I've heard bad reviews on the National Hotel (overpriced, not clean, poorly maintained, bar is loud late).
Lots of places don't have AC, so check that out if it's important to you. Yahoo Travel has a good summary of hotels and customer reviews.