Besides any of the standard hotels and motels offered there are a few out of the way/cheap options
Forest Lake Motel
Located north just outside of El Paso. Single story motel. They offer hourly and nightly rates that don't seem to have kept up with inflation. $5 an hour or $35 night/day rate. It is just close enough to Fort Bliss and the Airport that you are sure to hear lots of planes taking off. It is rated 1.5 stars.
A few reviews:
"Someone walked into our room at midnight! Never staying here again!"
"Owner didn't seems surprised our room wasn't clean."
"Owner came into our room and took our television without an apology to give to another couple staying two doors down!"
"Noisy and full of weirdos"
"Everyone minds their own business I stay there regularly"
Manner House Motel
This oddly named motel features a large oriental style sign. Located on the west side of El Paso near the 1,000 steps hiking trail. It features itself as being within "travel distance" to scenic mountain overlooks and activities. Single two story building.
$49.95 a night. It has no rating. There are several photos posted, one of which shows a window near the office open and what appears to be a large blood stain on the wall inside.
Reviews:
"Owners don't speak english. TV was coin operated."
"Hows this place still in business?"
"Dirty rooms, negotiable rates, no night staff, perfect!"