Part climbing, part back packing question

Hey there,

So I am interested in going down to NM with my roomie for a while, maybe do some climbing, but also to do some back packing (the two dont have to be in the same location).

I have already got some insight on spots to climb, but not for back packing.

anybody have any recommendations on where to go for a 2-3 day back packing trip? preferably in the northern part of the state?