Stew,
I think that's correct--North-northwest of the Chinati Mountains--almost due northwest of Chinati Peak.
They're on the Interwebs at www.chinatihotsprings.net. Their "getting here" link/map is a Google Maps base and zoomed in it also shows the spring itself by an older name "Ruidosa Hot Springs".
The "non WTW" route to reach Chinati HS is south on US 67 from Marfa to Presidio, thence a sharp hook back to the northwest on FM 170 to Ruidosa, thence 7-8 miles on gravel Hot Springs Rd to the "resort" (which perhaps I should not put in quotes since it is indeed a nice, if rustic and elementary, place to visit).
But the manly (or womanly--Hoyden) route from Marfa is southwest right out of town down FM 2810 (Pinto Canyon Rd), paved across the plateau for a ways, then turning to gravel and descending into the Pinto Canyon. It runs the canyon to a point close to Ruidosa, then another road branches north-northwest to the Springs. You can easily find YouTube videos of folks riding Pinto Canyon Rd on dual-sport bikes or in trucks or SUVs.
I'd had a nice chat with one of the Chinati caretakers who said most any reasonably high clearance vehicle can handle the Pinto Canyon route from Marfa and further said she runs it regularly in her 2WD Tacoma. Heavy rains cancel all bets, not due to mud, but instead due to the several normally dry washes crossed by the road which have no bridges. Other intel indicates Pinto Canyon Rd is heavily watched by the Border Patrol. One look at the maps shows the paucity of other routes out of the river bottom canyons so one can readily see why Pinto Canyon Rd would be favored for illicit human and other cargo.
The same individual spoke glowingly of some of the short canyon hikes accessed from the resort, including the "Art Canyon".
All in all, Chinati HS seems like it would be a fine place to visit, and a "no hookups" camping area is among their advertised accomodations. We were intrigued by one of the modest cabins with its own large stock tank fed by the HS waters.
Let me know if you can't locate it.
Foy