it's pretty sad that i lived in new mexico (albuquerque and santa fe) for 7 years and really couldn't make any non-touristy suggestions..it really depends on when you go tho..depending on the time of year there is spanish market, indian market and fiestas/the burning of zozobra in santa fe and the balloon fiesta in albuquerque which is the most photographed event in the world
definately walk around the plaza, there are a lot of galleries and the loretto chapel
theres the taos pueblo, and el santuario de chimayo
madrid is a little artsy community outside of santa fe heading towards albuquerque
the drive from albuquerque to santa fe along the turquoise trail is supposed to be beautiful
as already mentioned, if you are into gambling there are a lot of indian casinos..the newest one i think is sandia casino right outside of albuquerque, its new so its really nice..
i found this site with a lot of good stuff in it..
http://www.roadsideamerica.com/map/nm.html
i feel really stupid right now not being able to think of any really good suggestions (i guess i've just blocked that state from memory or something)
if you want restaurant suggestions tho, let me know..i'll see what i can come up with