I hoep you don't mind biking up (or down) hills...especially in the northern New England states, there isn't a whole lot of flat land.
How large is your Do you feel comfortable camping without hookups? A good many of the state parks have no or limited hookup availability; in particular, none of the Vermont state parks have any hookups. Most do have dump stations and water fill stations and shower houses.
Avoid roads called parkways as generally they have low clearances and are usually forbidden to RVs and trailers. Avoid the Boston area tunnels (I-90 and I-93 around the city center, primarily) as propane is restricted from them and the penalties for carrying it are quite stiff.
I agree with Crowe on pretty much everything said about Boston; lots of historical interest and cultural interest there. You do not want to drive through Boston if you can help it; take public transit, which will be much easier and quicker and probably less costly than paying for parking downtown. I often park at the garage at the Alewife station when I want to go, but that's far from the only option.
In Vermont, the Groton state forest and adjoining state parks (there are a number of them) are all interconnected by some nice hiking trails and a couple multi-use trails. The view from Owl's Head is quite nice, and there's a really neat little CCC stone shelter at the top. The area in general is fairly far off the beaten track, so there aren't a lot of services in the close vicinity.
Mount Ascutney is a nice hike; climbing the mountain is a reasonably strenuous day hike, or one can drive to the summit and hike around a series of trails there. This is a justly rather popular area, with many good viewpoints and an observation tower that has a 360 degree panoramic view. There is camping at the state park at the base.
Burlington city North Beach park has a campground (with hookups), a very nice beach on Lake Champlain, and the Burlington/Lake Champlain bike trail goes through the park. The bike trail is pretty long, a couple dozen miles I think, and getting to the Lake Champlain islands via it and roads is quite practical if you're up for a decently long ride.
There's a lot to see in the White Mountains of New Hampshire. Driving the Kancamagus Highway is a fine way to spend an afternoon or a day, and there are a bunch of hikes of varying lengths one can take from the highway (some very brief strolls, some longer). Ascending Mount Washington by the auto road or the cog railway (or, I suppose, on foot) is also a great way to spend a day.
The Maine coast has a lot to see. Bar Harbor and Acadia are an obvious stop, but there are a number of other interesting towns along the coast. Get too far from the coast and there are a lot of logging roads and not much else, though there are some places to camp in the north woods if you'd like to be quite alone and your RV isn't too large.
On the way out or back, you may wish to spend a day or two or three at Letchworth State Park in New York. It's exceptional; it very well could be a national park, in my opinion.
