There are lots of BCC kids in the Village, as well as kids who go to independent schools. In fact, all of the neighborhoods discussed above, Kenwood, Somerset, CC Village, and Edgemoor, have a mix of public school and private school kids, though the mix varies . Somerset might be at one end of the spectrum, with most kids attending public, and Kenwood on the other end, with most in private.
With re to housing prices, I agree that Kenwood is pricier b/c the houses and lots are more uniform in size and style. Kenwood was built by the Miller Companies as a single development, whereas Somerset has developed over time without any single builder dominating home construction in the neighborhood.
Kenwood, Somerset and Edgemoor all have pretty easy access to the trail and residents from all 3 n-hoods use it extensively.