Well, most of us in Albuquerque know about the crest road. This road winds its way up to the Sandia Crest from 6000ft to 10000ft. It ends at the top. You can pretty much go as fast as you want since there is really no police presence much, however, you won't get much over 50mph because the switchbacks come fast and there are many many. So, If you like to turn, this is the road. Very sharp switchbacks.
There are tons of New mexico highways that just turn into dirt roads after a while that are good for sliding. One in particular that you can get going pretty fast on and is pretty safe as far as turns is NM112. It is northwest NM connecting US550 from Cuba to US 64 near Tierra Amarilla. It abruptly turns into dirt about 1/4 way from the south and you can get some really good speeds and throw your car into some fades. Beware one section has a few quick turns that fall off short cliffs though...otherwise its flat with high mesa scenery.