We want to do some short, kid-friendly hikes (ages 2, 4, 8). Want to be able to access the mountains (not too snowy) but it also not be overly hot. Also, is there enough in this area to keep us busy for a week? Thanks!
September would be my suggestion - after the Labor Day holiday weekend if you can manage it. By October I think you'd risk the beginning of snowy weather in the mountains.
There's plenty to keep you occupied in and near Ouray itself. The Colorado Rte. 550 corridor is known as the "Million Dollar Highway" and is one of America's great scenic drives any time of year - the second half of September is usually peak season for fall colors, and there are hikes galore depending on your fitness level.
Parts of the route can be a white knuckle experience for those not accustomed to mountain driving - ie lots of sheer dropoffs with only occasional guard rails, etc.
Nice side trips I can suggest would be to Black Canyon of the Gunnison NP about an hour away, and the very pretty little mountain town of Telluride - also about an hour away. There's a series of cable cars there that the kids in particular might love, plus it's just a fun way to get around before the serious ski season begins.
I agree with the mid September suggestion. The fall colors are beautiful at that time. If you are near Durango, the train ride to Silverton and back is a lot of fun especially for the 4 and 8 year old.
Do your children go to school? That might be a factor on the time of year you’re asking info for.
As someone who lived in western Colorado for 35 years, 35 miles from Ouray, I'll just say that one way on the Durango-Silverton train was PLENTY for me and I think even that might be too much for young children. There is a bus shuttle which only takes an hour and a half (versus 3 and a half hours on the train).
I think there's plenty to keep you busy for a week. It's a gorgeous area.