Mike: First, I am assuming that you will not be taking your boat around the seaward side of the Cape; that is some challenging sailing, especially for a small boat. The elbow of the Cape is known as a graveyard for boats; is it your plan to sail Mass Bay, or do you have a particular Cape destination in mind? In any case, it will take you about three days to sail from Branford to the westernmost portion of the Cape in a 22 foot boat.
I can give you some insight into what you will find along Conn and RI shores, but a lot depends on your willingness to sail at night. If you are a daytime sailor, then I suggest the following: Day 1: Branford to Groton, either the Shennecosset Yacht Club or Pine Orchard Marina. That will take you a good five to seven hours, depending on wind and tide. If you don't want to sail that far, go to Westbrook, and either anchor out behind Duck Island, or tuck into Pilot's Point Marina. Another option if you don't want to sail that far in one day is to go to Cedar Island Marina in Clinton. Day 2: from any of those options, sail to (in order of distance) Stonington, Watch Hill, or Newport. There are places to anchor in Stonington and Watch Hill; I don't know about Newport, but there are plenty of transient berthing and mooring options there. From Rhode Island, you can get to Buzzard's Bay in less than a day. I have never been there, but it is supposed to be beautiful. From what I hear, the winds are strong and the tides stronger, but the Cuttyhunk Islands are reputed to be undeveloped New England wonderlands. The Cape Cod Canal is at the eastern end of the bay, and I have been told that the currents are a beast; however, that may be the only practical way to get a 22 foot boat into Mass Bay (aside from trailering). If you have any specific questions about the places I mentioned, I'd be happy to provide more details.