One thing I forgot to mention---when you're heading for Gay Head, just before or after the town line (it's been a few years), there's a wonderful natural spring with clear, cold water. Make sure you bring an empty water bottle with you. People come from all over the Island to fill gallon jugs there.
I'd take a left onto Moshup Trail just after the spring, and ride that road to the cliffs. Lot less heavily traveled.
I don't think it's quite 45 miles R/T from Edgartown to Gay Head, unless you extend the ride into Lobsterville. Probably around 36-38 miles.
I'm trying to remember how far out towards West Tisbury and Chilmark the south bike path goes. There are some things along South Road that are worth seeing---Alley's General Store in W. Tisbury, the "field of dancing statutes", vistas from the road towards Tisbury Great Pond and the ocean, the famous Chilmark cemetary with some celebrity graves (including John Belushi's), the Chilmark Store, the scenic overlook at the back of Menemsha Pond (on the only hill worth mentioning, and then more for inexperienced riders to worry about). I think if you head out early enough in the AM, you can beat a lot of traffic on the roads. People are on vacation and tend to sleep in, and the first day-trippers won't be arriving until mid-morning.