A few places in Groton I compiled while working there:
Abbott's in Groton has excellent lobster. BYOB. Prices aren't bad, a little on the high side, but definately worth it if you like lobster. http://www.abbotts-lobster.com/
The same people own Costello's Clam shack, which is less lobster, more clams, mussels, etc. http://www.costellosclamshack.com/
The Spot, located on Route 1 in Groton is good bar food. Pretty typical bar menu, with a few interesting additions.
Over in New London (less than 10 minutes from Groton) is Saeed's which has mediterranean food. Very good gyro's. http://travel.explorenewengland.com/restaurants-view-8604403822-saeed_s_international_market-new_london-ct.htm
In East Lyme, about 20 minutes or so away, is Flander's Fish Market. I never have been there myself (not much of a fish fan), but coworkers raved about the place. http://www.flandersfish.com/
In Mystic is the Voodoo Grill. Great corn chowder, and some interesting things like alligator on the menu. It's in a great part of Mystic to walk around after dinner too. http://thevoodoogrill.com/
The Bank Street Roadhouse over in New London has a great pulled pork sandwich, and is right on the river. http://www.crosbyrestaurantgroup.com/...
What ever you do, stay away from the Casino's. You won't find anything decent there. Also stay away from Go Fish in Mystic. I hope this helped.
Its been mentioned on these boards before - Noah's in Stonington Borough. Excellent selection of seafood dishes that change base on what's the freshest. The owner travels so the influences vary - he's influenced by everything from Portuguese, French, Morrocan, German. And all the desserts are housemade - as is the bread. And they have a bar.