Check out Colorado Springs.
Homeschool- From what I understand, the homeschool laws are very reasonable there.
Gymnastics - The U.S. Olympic Team trains in Colorado Springs!
Interracial family - there is a large military presence in CS, which in my experience, there are a lot of multi-racial marriages in the military. I and my wife are the same race, and I feel in the minority among the people I work with.
The population is somewhere near 400,000, so to me that is an in-between size city. I have heard wonderful things regarding the traffic there, relative to VA traffic. There are 5 Targets in CS. Also, it is about an hours drive to Denver, if you needed something at a bigger city.
Cost of living is very good, IMO. The median home price is about $180,000