The top five places to visit in New England that I know of:
1. Autumn leaves. Come by in the fall, usually in October, to look at the color show the trees put on. They start to turn in the north first; they're beginning to turn in southern Connecticut now. Local news stations sometimes track when the peak colors have arrived. The Pachaug State Forest and surrounding area has some oaks that turn deep crimson, late in the season.
Some years are much brighter than others. It depends on what kind of weather we've had over the summer. This year is looking promising.
2. Old Sturbridge Village, in Massachusetts. A very large open-air museum replicating a community in colonial America. They have livestock, harvests, craft demonstrations, music, and more. Fascinating.
3. The Mystic Seaport and Aquarium. Here you can find the whaling ship the Charles W. Morgan, more about early American life (this time along the coast), and a fine display of marine life.
The Morgan is said to be haunted, but I didn't notice anything when I was there.
4. The White Mountains in New Hampshire. Here are trails through the mountain, fine scenery, and a refreshing absence of mosquitoes (since all the water is flowing). The glacier-sculped twisted basins, down which icy streams still flow, are curious and interesting.
5. The Race. You need a boat for this.
The Race is a fast, strong confluence of tidal currents at the eastern end of Fishers Island, marked by Race Rock Lighthouse (also said to be haunted). The intensity and complexity of the currents can make the water behave in fashions you'd never anticipate, and it's never the same twice -- it depends on the tide and the weather. Sometimes you may end up looking at ordinary waves. Other times, a stream of glass-smooth sea may be flanked by an area of strange vertical chop, where the water dances straight up into nearly-pyramidal waves that throw droplets into the air from their peaks; nearby, there may be a standing wavefront. Weird and wonderful, if you get there at the right time.
A lot of charter fishing boats visit the Race. I once caught an *enormous* striped bass there -- 53 lbs! (OK, it was 13 lbs when I caught it, but, of course, it's grown with every decade that's passed.)