My husband and I are coming to Groton in November to visit our son who is at sub school. Any tops fir us on cool things to do in the area?

Cool things to do would depend on what you think is cool. I like museums and food, but to my sister "cool" things would be something like doing a zip line or atv riding.
Some people like Mystic Seaport, or Mystic Aquarium, or just shopping around Mystic Village. Newport is about an hour away and I always enjoy taking a tour of one of the mansions, walking the Cliff Walk, and getting something good to eat.
This is an overview for the Mystic area (Mystic is the name of an area made up of parts of Groton, and I believe, Ledyard)
Agree with Ruthie, Mystic is a great place to spend the day. Lots of shops, restaurants, and history. take a camera, lots to shoot. Not really my thing but you have the casinos in the area. Mohegan Sun is better IMO - http://www.mohegansun.com/gateway/index.html
Cheers
Day, weekend, week?
You might enjoy exploring one or both of our 2 local casinos - good people watching, quite a variety of restaurants, and some (mostly high end) shopping. Its fun even if you don't gamble.
Agree with all of these recommendations as well as visiting the Nautilus Sub near the sub base.
Also, you could look at the Esses Steam Train / riverboat combo and see what they are running in Nov (may just be the train or even closed for the season).
Don't know what your interests are but there is a very good museum near Foxwoods Casino. The Pequot museum.There is BF Clyde's Cider Mill - the oldest steam powered mill in usa- that is always an interesting place to go to.
Just google these names for directions
Into BBQ....
Visit CHESTERS BARBECUE--Best smoke house anywhere around.
Located 943 Poquonnock Rd. in Groton.
Bring your son and enjoy !!