As bhblaine points out, it is a good wheeling area and there are some great places to see. I fly fish and jeep that area from the Colorado border down way past Taos. There are many forest roads, hot springs (along the Rio Grande), meadows. They are remote and beautiful.
There are so many places, too many to mention. I would contact Carson Natl Forest for their map which has the roads marked. Word of caution, you will want to see what is open to the public as much of NM forest have been closed.
As you may have heard, there has been devastating wild fires in Az, Tx and NM. The area has been much dryer than normal (we have not had rain where I live since last Sept) and wild fires have already taken out hundreds of thousands of acres of forest in AZ, NM and even here in TX where we had pine forest in high mountains in west Tx.
Cabresto Lake has also been closed for construction of a new dam that will make the lake many times larger.
Sorry to leave you on a sad note. I have canceled my NM trip this year (but still planning on Colorado). AND rains could start and it be different in even the next few days.
Check with the forest service. Good Luck.