The majority of connecticut's coastline is sheltered by long island, thus forming the sound. The result of this is that beaches are nor your classic beaches although some are still quite nice. Research which ones you want to go to first though, as some (for instance my home town) only allow access to residents with permits. Others allow access to all, but only grant parking to residents.

Mystic/groton is a very nice town with nice beaches. However I find it rather uninteresting after a day or two. Traffic isnt so much an issue up there, but nice lodging with the chains likely will be. Look for a bed and breakfast.

My preference for such a trip would be to spend at most a day in mystic (nice aquarium, scenic town) and then take the ferry out to block island for a couple of days. Block Island is a good time. Great beaches, good fishing, a couple of decent restaurants and reasonably priced B&Bs. Its a frugal man's version of Nantuck or Martha's Vineyard.