I can really only speak to rural Colorado, since that is where we wound up. Colorado is solidly blue-leaning at the state level, but varies greatly in its political leanings county-to-county. And county presidential voting trends tell you an awful lot about the quality of government services in that area, including schools and public education. That is at least true in the rural counties outside outside of the I-25 urban centers. El Paso county (contains Colorado Springs) leans red, but I am sure it has some good schools within it. But if you are wanting to be out of the city, I would pay attention to this map:
The counties that are rural and red will have the local politics dominated by libertarians with conservative, small government views. These counties will have relatively low property values, relatively low taxes, relatively little money available and thus relatively poor government services. The schools will not be great, and if your kid's education is important, you'll want to not rely on public education in these areas.
If I was looking to raise a family outside of the cities in Colorado, I would target La Plata County in the Southwest (Durango area) or Chafee County in the center (Salida/Buena Vista area). The resort areas like Breckenridge and Vail are wealthy and have good services/public education, but in my experience with my family, they don't feel like real towns with families and community. 90% of the population are vacationers, seasonal workers and wealthy second home owners who are only there part time. Great to visit, but you and the rest of your family will feel isolated in a sea of transient passerbys if you live there.
Durango and Salida are great rural communities and my two favorite towns in Colorado. Both are politically moderate, place value on things like public education, are priced within the reach of someone coming from a suburb of Austin, and are near everything you think about when you think of Colorado (mountains, skiing, fishing, hiking, mountain biking, rafting, etc...). They are small, but big enough to have most of the things you want like a hospital, some decent restaurants, etc...
Durango is larger (19,000 vs 5,800) and is a bit more accessible to the outside world as it has a small airport with commercial flights. It's a college town (Fort Lewis). Salida has a small community college.