What does your family like to do? We don't have any place like Disneyland or anything...

But here are some things off the top of my head.
There lot of hiking, biking tours and kayaking /canoeing places
Around Burlington and surrounding area:
Great Bike path along Lake Champlain
Take a ferry or some other boat tour of Lake Champlain
The Echo Aquarium and science center (although your kids may be a little old?)
Champlain Chocolates (I think they have a tour)
Cruise around Church Street and downtown Burlington
There is a roller Skating Rink, go-karts, and climbing centers
Hike up to Mt Philo
The Shelburne Museum
Magic Hat or a ton of other small breweries (Although this would be for Mom and Dad :

A Lake Monster’s baseball game (Class A I think?)
Morgan Horse Farm
Cruise through the Champlain Islands
Stowe’s Alpine slide
Jay Peak has an indoor water park and maybe an alpine slide?
Racing (car):
Thunder Road
Devil’s Bowl
There are a ton of Concerts, festivals and fairs during the summer. A couple of them are:
Champlain Valley Fair
Addison County field Days
The Lake Champlain Maritime Festival
Grandpoint North festival (music)
Rock of Ages Granite Quarry tour
Wilson’s Castle - Proctor
The Fairbanks museum and planetarium – St Johnsbury