The area around Frisco/Breckenridge/Vail/Copper Mountain (the front range) is very beautiful. I've only been there during the winter and fall for skiing and snowboarding, but I know during the summer they do a lot of bike rentals out of the same shops. Hiking and camping seems plentiful in the summer months. That's pretty much the only area of Colorado I've been to though. I hope you can find a good vacation spot for the family, good luck!