lived here my whole life, and don't intend on leaving! two hour drive from albuquerque in any direction will put in nice quiet mountain country!
A nice place to go if family is coming along is Ruidoso; lots of trout, deer, elk, bear mountain lion, coyote and turkey plus it has nice places for shopping and trinkets in town. Ruidoso is about a 2.5 hour drive south/east from albuquerque. the town is kinda touristy, if you know what i mean, but its nice.
any where up in the pecos area is nice too, but that's putting you in "remote" areas without amenities (again, if family is in tow). you can be in the pecos wilderness in about a 2.5 hour drive north of Albuquerque. same wildlife here too
plus big horn sheep!!!
West of Albuquerque is Mt. Taylor. again, about 2.5 hour drive. the same wildlife there minus trout fishing.
to the far north is chama and toas. toas is much larger then chama with shopping and skiing too. Taos reminds me of a mini Santa Fe. Chama got something like 10 or 11 feet of snow this last winter! that's a lot for us New Mexicans! here's a picture i took in early fall on the road between Taos and Chama at about 10,000 ft elev...