There are some fantastic roads in the area. If you can stay in Silver City you'll have better access to these roads, and besides, Silver City is a much nicer area. Las Cruces is not a very scenic place. Anyhow, NM 152 is not to be missed. Pick it up near exit 63 on I25 or better yet, get off I25 at Hatch and take NM 26 west to NM 27 north to NM 152. Ride NM152 into Silver City.
The other great ride in the area is best done with Silver City as the starting point so I'll describe it from there.
Take US 180 north to NM 78 which becomes AZ 78 to US 191. US 191 used to be called the Devil's Highway when it was US 666 prior to a number change. US 191 is one of the best roads in the country. You'll head north past on of the biggest copper mines in the country and then you are in the twisties for mile after mile. You can reconnect with US 180 at Alpine, AZ and ride it back south to Silver City.
Let me know if you'd like more specifics on these routes.