West Yellowstone - Playmill Theater (there's a location there too); Grizzly Bear Discovery Center; go and walk the main street and window shop / look at stores and eat ice cream; IMAX theater (if it's still there?); Quake Lake (short drive outside of the city)

Island Park - you can rent canoes at Macks Inn and then they'll drive you ton a launch point a little ways below Big Springs, then you run the river back to Macks Inn (it is a very slow and easy going trip...no rapids); drive to the top of Sawtell Peak; you may be able to rent 4 wheelers in Island Park...there are plenty of trials;

You could also do a day trip to Jackson Hole and the Grand Tetons area. There are plenty of walks / hikes in Yellowstone that are short and not very rigorous.

My family has been frequenting Island Park for about 25 years. It's one of our favorite getaway places.