CT has pretty extensive dedicated bike trails. You can ride from New Haven to Southington (24 miles) on paved bike only lanes, then a 10 mile road stretch with shoulders up to Farmington, then from Farmington a 64 mile stretch of dedicated bike road to Westfield, MA (total about 108 miles).

The Airline Trail has two parts in Eastern CT: a really nice crushed gravel section (20 miles) from East Hampton to Willimantic, then after going through Willimantic, a shorter section north of there. THe Hop River Trail goes from Manchester to Willimantic-- a very nice ride.

The road I live on (rt 154) has comfortable shoulders for a lot of it's length and goes through a bunch of pretty villages in south central CT down to the shore.

Do you ever use Google Maps to find bike trails? You'd be surprised how many there are, I think.