Definitely hit up the aquarium. As far as I know, there is only one real "museum" in the area. I do believe that there are smaller museum like attractions in the area. We've take our kids to a place called World of Wonder in Ft. Collins. The Children's Museum. I've heard of the Wings Over The Rockies Museum, but I haven't been there.
I second the Museum of Nature and Science. I'd also check out the Denver Botanic Gardens. I've been a couple times and really enjoy it. Also, you should know that the museums have free days, check it out: :: Welcome to SCFD: Making It Possible ::
The art museum is free this Saturday, Nature and Science is free Sunday.
For the shorties, definitely the Children's Museum. If you want a two-fer (not a buy one get one free, but 2 in the same block), hit up the aquarium at the same time.
On the outskirts of downtown is the Firefighter's Museum. Not sure of the hours, but it's about 15th Street and Tremont.
Don't forget the Colorado History Museum - 1560 Broadway.
Denver's Art Museum is amazing. Even the architecture is phenomenal.