Hi Bobby,
We met last year when we were both moored in Edgartown. I was going to suggest Pine Island to you, but you beat me to it. I believe that is a great choice and the state ramp there is good as well. All the info that Brian B. gave you is spot on. If you do decide to go around to Old Harbor, it is small, but the holding is great. The bottom of the harbor is shaped like a cereal bowl. You can anchor stern in to the breakwater, tie a line to the breakwater and put your stern right where the bottom comes up. You can walk off your boat and into town at low tide.
Fishers Island is nice, but largely private. You can find a great anchorage in East Harbor. Clear, clean water, great swimming and calm. You can go ashore in West Harbor, but there really isn’t much there. Fishers Island Sound is my favorite place on the planet. If you have engine trouble or other problems where you need a yard, look up Noank Village Boatyard. They are Volvo Penta and Yanmar certified and their service is top notch. I kept my boats there for fifteen years and will be going back at some point - hopefully soon.