Jon - You probably want to make a trip out to Hueco Tanks, out east of El Paso. It's a great place to hike and climb around, though they generally frown on collecting artifacts. There is some cool rock art in the area. You can also hike the Organ mountains and there's also a lot to do and see there. Out by Deming NM there's an old Ft Cummings that has some history in the area and is generally far enough out that no one cares what you do. Also, if you've never been to the area before, White Sands and Carlsbad Caverns are places you really should visit. If you want to head into Lincoln Co NM up in the mountains, Cloudcroft, Riudoso, etc, there are some good fossil hunting places but this time of the year it's going to be a bit cold. In 3 months there are certainly enough places to look and things to find to keep yourself entertained.
good luck.
Joe