Welcome to Massachusetts.
I would recommend a weekend trip to Martha's Vinyard. We did this trip last labor day weekend-- it was a perfect time of year. The water is at its warmest, the campground uncrowded, etc. Park in the standard satellite lot for the Woods Hole ferry, and pick up the Shining Sea rail trip immediately adjacent to the parking lot. This nice path goes ~2.5 miles directly to the ferry. Nice views of the sound and an opportunity for a swim along the way. Take your bikes over on the ferry, leaving your car behind. Either ferry (Vineyard Haven or Oak Bluff) will do, and no reservations are needed as a walk on. Ferries leave every 60-90 minutes, so planning is easy. There is one campground (very nice but a little $$ for a campsite) near Vineyard Haven, which we used. Since it's so close to the ferry, we took a lot of our car camping gear over on our bike. There is also a Hostel, although it's a bit far from the towns. And many hotels and B&Bs, of course.
Edgartown, Vineyard Haven and Oak Bluffs are all very nice. These three towns are all accessible with short (<=5 mile) non-hilly rides. A lot of the riding is on bike paths along the roads. Chappaquiddick is also supposed to be a nice intermediate distance ride (mabe 20 miles rt), but we didn't have time for it on our visit. We also did a very nice and scenic, somewhat hilly loop ride out to gay head. That ride was 35-40 miles rt.
I always love leaving my car behind and taking my bike on a ferry to an island. Not only is it practical (Martha's Vinyard has limited roads and bad traffic in it's towns), but it is somehow romantic. Your young daughter will probably get a kick out of arriving by boat and riding away. It also instantly gives me that away from my car/ on a real tour feeling.