Natural hot springs in northern NM a bit off the beaten path?

Jemez Springs is worth a shot.Try Los Ojos Restaurant & Saloon while you're there.

Eh, during the summer, there aren't many places off the beaten path. The Jemez Hot Springsarea has quite a few "off the path" sort of places, and there are campgrounds nearby, but most resident New Mexicans know of these spots, so if solitary/romantic is what you're looking for, it'll be hard to find. Most of the springs are often filled with younger, college age folks who, on occasion, seem to be missing their clothes or are slightly less than sober. In all, though, I'd say worth the trip. 

Ojo Caliente Mineral Springs Resort & Spa is an ancient natural springs, now with a very comfortable, reasonably priced hotel and well-maintained pools and services (like mud bath), and restaurant. Very much a locals' place. 

Ojo Caliente is THE best hot springs.