Another biased vote for Colorado..............
We also have a 6yo (girl) and there are tons of things to do in Denver. But, we live in the mountains and instead of having a problem with boredom (ha ha) we have a problem with too much to do and too little time.
Steamboat Springs is awesome. Hiking, Biking, swimming, fishing, tubing, etc. We have a rec center where the pools are heated by natural hot springs. It's hard to swim in all of the 'cold' pools we encounter on vacation.
I'll try to list all of the things available for families in Steamboat in the summer;
hiking, tons of trails
biking, trails and the core trail which is a paved bike path from one end of town to the other
swimming, at the rec center, at Strawberry Park Hot Springs, in the river
tubing in the river, dependent on water levels
several nice parks to play or picnic at
really nice library, worth visiting even if you're not a reader
large variety of musical performances, Strings on the Mountain for one
gondola rides to the top of Mt. Werner (hiking, biking, lunch, etc. at the top)
Saturday farmer's market
There is just a lot to do in Steamboat. Here is a link to the local newspaper www.steamboatpilot.com
Have fun wherever you go!