Sorry about the Bronco's fan thing

But I'm sure you'll catch a great game!
Gillette Stadium - it sounds like you got some good recommendations from others who have stayed in or live around the area. The stadium is attached to and next to an outdoor mall - lookup Patriot Place online for a complete listing of stores and restaurants but off the top of my head - Cinema/Movie theater, Trader Joe's, Michaels (or one of the craft stores), Christmas Tree Shop, Staples, Bass Pro (fun store to just walk around in), the Pro Shop which also has a Museum in it (cost associated) of Patriots memorabilia. 10 minutes down the road is Wrentham Outlets if your interested in shopping... I highly recommend the apples at Rocky Mountain Fudge Shop
Boston
Aquarium - I would skip. Your on a mini trip here so I would go for maximum impact. Aquarium is high cost, time consuming, and IMO not enough return for the what your paying. Biggest sites here are the penguin exhibit, huge tank in the center floor to ceiling 3 stories high, and the sea lion show which is kinda short.
Duck Tours - good or bad rating really depends on who is driving the duck. We've been on several and had good and bad experiences. The Elvis impersonator and Crocodile Dundee act a like were two of the better ones. Not cheap but I would recommend this route for your kids age level and the amount you get out of Boston. I think you would see the most of Boston while also getting the history of several of the sites. Also would give you an insight of things you might want to see on a return trip. You wouldn't have to drive in bad traffic, walk miles and miles, and you get entertainment with it! They sell duck beaks where you board for the kids - they will love them, you, not so much

There are 3 boarding places - aquarium, museum of science, and prudential center. The aquarium is an abbreviated tour for the same price as the longer other 2 pick up spots. I highly recommend if you choose this route that you make a reservation online/prepay so you know you have a seat and have an assigned time vs. walking up and possibly having to wait, find a way to kill time. Your kids are also a great age for this because they will get to drive the duck during the water portion of the tour - bring your camera for this photo op and the kids LOVE doing it.
Musuem of Science - love it but my main question is do you want to see Boston or do you want to go to a museum? Large museum, can kill a 1/2 day here or the whole day. My kids love the electricity show. Loud and you get to see lightning indoors.
Blue Man Group has a show in Boston at the Charles Playhouse
We live about an hour from both Gillette and Boston so we frequent them several times a year (I was at Gillette and Wrentham last week!). Our ideal trip when the kids were younger was to take the train into South Station, walk over to the Children's Museum, spend 1/2 the day there (always got a hand stamp in case we wanted to return same day). Then walk over to the Aquarium to see the outdoor seal/sea lion exhibit (free). Then continue our walk over a couple blocks to Fanhueil Hall - shops, food food and more food, live entertainment a lot of the times - outside musicians and other artsy type stuff. Then we would walk back to South Station and take the train home.
If you had a vehicle, Boston isn't your only option. Boston by MapQuest is about 35-40 minutes. You could also head to Plymouth Plantation, Plymouth Rock, the ocean (about 50 minutes) - I know not beachy weather but enjoy heading to the ocean anytime I can. I guess it really depends on what your looking to get out of the trip.
Have fun with whatever you decide on... we love Boston and make it a point to go there frequently.