Las Cruces is popular as you say and therefore they do have a great selection of hotels to choose from.
I would suggest taking a look at the
Las Cruces Hotels pages. This lists several hotels in the area and should make it easier for you to find accomodation to suit you. If you are looking to be in the heart of Las Cruces, the Best Western Mission Inn would be a good choice. For something a little closer to nature the Vacation rentals Las Cruces has villas, cabins, homes, or condos and offer more privacy and space than staying in a hotel suite