There are many children of all ages in Floyd County. Most kids go to public school. Floyd County public schools are not exactly academically rigorous, but there are very little of the the "issues" one finds in more populous districts. They do have good sports programs. There are some home schoolers, both religious and non. Blue Mountain is tiny, expensive, and also not academically rigorous, but no doubt very self-affirming. Regardless of your choice, the responsibility for real education will fall to you.
A good place to run into little ones is at the playgrounds on a nice day in summer or weekend. For playgrounds you have to go to one of the churches, elementary schools, or the park outside town (north on Rt. 8 from the stoplight). Sadly, there is no public park in town itself. I recommended one for the former grocery parking lot next to the Blue Ridge Diner, but they kept it a parking lot (in fact added even more parking on the other side of the building) and then called it, with unintended irony, the "Village Green."
Floyd is not particularly bicycle-friendly.
The
library (which is a good one for a small town) has many activities for children. Stop by and get a schedule of the story hours and so forth. Also check out the
June Bug Center.