Oh, Joy, New Mexico! one of my favorite states for riding. Especally the north central portions, anywhere within a hundred miles of Taos.
If you're going to be there in early September, I strongly suggest you check out the New Mexico BMW club's annual rally, the Bavarian Mountain Weekend, located not far north of Sante Fe, in truly one of the best motorcycle roads and scenery I've experienced. Take a look at
Some recommended riding would include north from Sante Fe, on "the High Road" (historic route, photo attached) to Taos, through the villages of Chemayo (famous for delicious chili's) Truchas (where movie "The Milagro Beanfield War" was filmed, a great movie by the way), and on over the mountains to Taos.
From Taos don't miss riding "The Enchanted Circle" about 125miles, a beautiful loop that includes Angel Fire, NM Vietnam Memorial (very moving), Red River, and more.
North and west of Taos, the routes to the towns of Tres Piedras, Chama, Dulce, and more are among some of the best unspoiled and undeveloped mountain scenery imaginable.
I've returned to this part of NM three times since "discovering" it in 2007, and plan to return again this year at least once.
I'll try to get some highway numbers this evening when I get home where my maps are.