It has been a number of years since I did an end-to-end Connecticut coast ride that took in a chunk of the territory you'll be traveling, but I can tell you that, at New Haven, I turned off Rt. 1 and made my way onto Rt. 142 then to Rt. 146 to take in some water views (my favorite scenery) and the towns of Branford, Indian Neck, Pine Orchard, Leetes Island, Guilford before heading back onto Rt. 1. I found Old Saybrook to be a nice place to spend the evening.
The next day,I got back on Rt. 1 to cross the CT River and then dipped back toward the water on Rt. 156, which took me through Black Hall, Sound View, and Niantic before dumping me back onto Rt. 1 at Waterford. Next comes the Gold Star Bridge, which you'll access in New London. If you need specific directions to get to the bridge's bikeway, I can provide them.
After the bridge, I can get you to Mystic using neighborhood roads and state parks that are much more pleasant than Rt. 1. Plan some time in downtown Mystic if you have never been there. It's my favorite place on earth.
Once you're in Mystic, you might as well just use Rt. 1 to get to Westerly, RI, as the little detours I have taken over the years were nothing special. At Westerly, make your way down toward Misquamicut Beach, which is in the same area as Watch Hill.
I've left out some details because it will be time-consuming to add them here and I'm not sure if you're looking to sight-see or to mash your way between the starting and end points. Let me know if you need any more info.
Have a great ride!