Find a local facility that boards cats or even "at-home cat care" from a kitty sitter on this page. Example:

Q: How would I find boarding for cats near Columbia, South Carolina?
A: You can find a list like this: Kitty Sitters / Boarding > Texas > Austin

Q: I'd like to find a professional cat sitter in Texas.
A: You can find nearby pros here: Kitty Sitters / Boarding > Texas

Albuquerque
Bolton Boarding Kennels, 2005 Yale Blvd Se, Albuquerque, NM 87106; (ID #274), call 505-243-6251; located in or near Bernalillo county  (see map)

Arenas Valley
MIS Amigos Pet Care Center, 11745 Highway 180 E, Arenas Valley, NM 88022; (ID #917), call 575-388-4101; located in or near Grant county  (see map)

Las Cruces
Argus Pet Center, 705 S Valley Dr, Las Cruces, NM 88005; (ID #171), call 505-526-3086; located in or near Dona Ana county  (see map)

Roswell
Roswell K 9 Ranch, 64 Mark Rd, Roswell, NM 88201; (ID #1170), call 575-622-0004; located in or near Chaves county  (see map)

Sandia Park
East Mountain Cattery, 5823 La Madera Road, Sandia Park, NM 87047; (ID #1438), call 505-281-0184; located in or near Bernalillo county  (see map)
website: www.myspace.com/eastmountaincattery; email: allpoints333*gmail.com (replace the * with @)
Cats Only Boarding Hotel

Truth Or Consequences
el Rancho Poodle Farm, 307 N Maple St, Truth Or Consequences, NM 87901; (ID #565), call 575-894-2017; located in or near Sierra county  (see map)