Honestly? Westerly, RI and its attached beach town Misquamicut might be the better option. Gorgeous beaches, not on the sound, and decent nightlife is available, I think. Westerly is also maybe the most New England of towns in the region and leans a little younger than Stonington.

Or maybe even further into RI to South Kingstown (college town) and Narragansett (beach town). Gansett can get a bit touristy, but it's mostly with people day tripping from Providence. Newport and Mystic draw more regional/national tourists.

If you want more city, Providence proper and New Haven both host Ivy league universities, have waterfront and night life. There are ferries that can get you out to block island from Providence (with a few hops), which I hear is a lovely trip. New Haven is the last stop on the NYC rail line, so it's not difficult to get into the city from there.

If you plan in advance, you can easily hit the entire coast via Amtrak. It's the one place in the nation that there's a working, practical rail line that can take you from NYC along the sound to New Haven, Mystic, Westerly, Providence, and into Boston. No car necessary.

Enjoy, eat a lot of seafood and pizza.