Mystic CT is a nice place to visit for a day or two. Mystic Seaport is a maritime museum with sailing ships mostly from the late 1800s and a small village with demonstrations of many of the skills associated with whaling, like cooperage, blacksmith, sail makers as well as shipbuilding.

There are also wineries in the area that do tours and if you are into casinos, Foxwoods and Mohegan Sun are glitzy Vegas style venues.

If you go to ctvisit.com you can find out what is happening all over the state, including fairs, shows, museums etc.

I think I'd vote Newport, but then I love old houses and history. Newport is very pretty, but it will be off-season, so check into if everything is open. I have no idea whether there is a time when the houses shut down, but I'd at least think about it.

I find the Cape or at least parts of it super-touristy and tacky. it could also be pretty cold.

Around New Haven, I found Guilford to be a charming town with a pretty green, worth driving through for lunch. You might also want to consider towns like Westport and Greenwich to stop in if you want an Eastern/Lower connecticut feel.

Unfortunately, I've never been to western Connecticut so no comments there, but to throw out another idea, what about Hyde Park and the Vanderbilt house in New York.

Some of the major mansions in Newport are open year round, though not all of them. You could easily spend a day with what's open then and taking the Cliff Walk. All are well worth experiencing -- I'd do an online look-see for those open in late fall.

Agreed that Mystic makes for an excellent day's visit. Both the Mystic Seaport and Mystic Aquarium are well worth going to. I'd check their hours for late October/early November, though, just to make sure they're open then.

The casinos mentioned above are pretty much like those anywhere else, though Foxwoods is also home to the very good and good-sized Mashantucket Pequot Museum and Research Center -- again, check online for most recent hours.

Other Eastern CT attractions to consider depending on your interests would be the Florence Griswold Museum (both a historic house and museum space, Old Lyme), Gillette Castle State Park (historic house with nice surrounding grounds, East Haddam), the Henry Whitfield State Museum (a house restoration, Guilford), the Lyman Allyn Museum of Art (New London), and the Submarine Force Library and Museum (Groton). Again, check for current hours at the time of year when you're visiting.