We liked the Amerisuites, but have since outgrown it (4 kids!). Not super cheap, but it had a pool (outdoor, not much good this time of year), included breakfast, and the staff was very friendly. Walking distance to the aquarium and seaport.
In Groton, we now stay in the Super8 right off I-95. Not fancy, but clean and again, includes breakfast. Cheaper than Amerisuites. Groton doesn't have a whole lot of good hotels, and IMHO, the prices are out of line for what you get. But, I grew up there (who you callin' a dump, monorail silver???), still have family in the area, and the Super8 sure beats my sister's house with her 17 cats!