We had family visit us this summer (DSinlaw and DBinlaw-forty something) and they really enjoyed the trip we made to Newport, RI. I was really surprised. We visited the famous Newport mansions and there are good restaurants and shopping. But I'm not sure what is shut down by October. I know the mansions are open year round cause we've been there in the winter. They have self guided tours with headphones so you can explore at your own leisure. There is a beautiful Cliff Walk on the shore that connects a lot of the mansions. Also open year round. It may be chilly depending on the weather. It reminds me of Ogunquit (Marginal Way) and the Maine coastline. Newport is geared for adults so if you have little ones the mansions might not keep their interest. This is about 1 hour south of Boston.
We spent a day in Boston and Salem, too. They really didn't like Boston as much as I thought. It was a lot of walking and taking the subway and they were not used to ANY big cities.
I love Boston! We live about an hour away. The freedom trail is good. The Old North Church in the north end is a nice walk and it's free. The North End is Little Italy in Boston. Lots of restaurants. Faneul Hall (also part of the Freedom Trail) near the Aquarium has something for everyone. Variety of food, shopping and street performers. The harbor is right there and you could take a harbor cruise, whale watch, etc,. And definitely take the Duck Tour. It's a lot of fun and you get to ride in the Charles River

So my sister in law and hubbys favorites were:
1) Newport RI
2) Salem MA
3) Boston
You are driving a lot for five days. Each of the trips listed above is about an hour from my house and it seemed like we spent a lot of time traveling each day. They were all day trips. (Unless you want to do a lot of driving.)
Sarasota Springs has gambling but it is a ways away And so is Vermont

MA is kind of boring except for the foliage and Yankee Candle in Deerfield, MA.
Connecticut has two casinos, Foxwoods and Mohegan Sun. We are not big gamblers but if that is your thing, they are both beautiful casinos/hotels. My mom goes all the time.
The White Mountains (as Patsfan suggested) is closer to Boston and is an easier drive than Vermont. Beautiful any time of year. Foliage does start to disappear mid October in NH. And its true. New England in the Fall is busy!!
My faves (with limited time)
Boston
Ogunquit, ME
White Mountains
or
Boston
Newport, RI
Foxwoods Casino, CT
My hubby's family were late risers and they didn't understand why everything closed early around here! 5-6 pm and touristy things close. Everything except the casinos

It's kind of like rope drop at WDW. Get going early, especially if you have to drive for 2 hours to get there.
So do you have family in Bedford, NH? It's kind of a small town. Just wondering. We've driven through it but there's not much there. Are you staying at a B+B or something?