Sorry life got in the way and we couldn't meet up. @Manona's suggestion to take a left on FR376 is a great one. The cool thing is that it dumps out back onto HWY 4 farther south. Then you can take a left and come up through Jemez Springs, where you can stop for some food or a soak in some hot springs/spa treatment.
So to summarize: Head up to Los Alamos and continue on HWY 4 past Bandelier NM and past the Valles Caldera NM (or stop in to check them out, if they are open) Continue up HWY 4 to the intersection with 126 (at La Cueva). Turn right on 126 and then go about 3.5 miles to the intersection with FR 376. Take a left and continue on 376 for a long time (20 miles or so). There is some nice scenery through there and you eventually will go through the "Gilman Tunnels". Eventually 376 turns into 485 right before connecting with Hwy 4 again. Total mileage on dirt is about 20 miles. The road is just a dirt road that I have driven on with my Lexus ES350 in the summer. Might be some snow and ice on it. Lots of little side FS roads you can go out and back on if you want slightly more interesting driving. But since you're not in a group, be careful. You don't want to get stuck and have to spend the night out there. It's cold and there is no cell service. To be safe, make sure you are prepared to spend the night (clothes, blankets, food, water) just in case. @Manona doesn't want to have a call out to rescue/recover/retrieve your frozen butt. If you happen to see a really cool diesel powered 80-series in Jemez Springs, that's hers.
So to summarize: Head up to Los Alamos and continue on HWY 4 past Bandelier NM and past the Valles Caldera NM (or stop in to check them out, if they are open) Continue up HWY 4 to the intersection with 126 (at La Cueva). Turn right on 126 and then go about 3.5 miles to the intersection with FR 376. Take a left and continue on 376 for a long time (20 miles or so). There is some nice scenery through there and you eventually will go through the "Gilman Tunnels". Eventually 376 turns into 485 right before connecting with Hwy 4 again. Total mileage on dirt is about 20 miles. The road is just a dirt road that I have driven on with my Lexus ES350 in the summer. Might be some snow and ice on it. Lots of little side FS roads you can go out and back on if you want slightly more interesting driving. But since you're not in a group, be careful. You don't want to get stuck and have to spend the night out there. It's cold and there is no cell service. To be safe, make sure you are prepared to spend the night (clothes, blankets, food, water) just in case. @Manona doesn't want to have a call out to rescue/recover/retrieve your frozen butt. If you happen to see a really cool diesel powered 80-series in Jemez Springs, that's hers.