From a strictly U.S.-Russian strategic point of view, we should agree to those demands so long as Russia agrees that it will not station any troops or other offensive weapons in those countries either, and that if it does, NATO is entitled to view such actions as aggression directly against NATO.
It won't be such a great result for those border countries, but there really is something to be said for having a series of nonaligned border countries between Russia and current NATO members.