A lot of the Rodeo folks put their horses up at the Legacy Center in Farmington Utah (20 miles north of Salt Lake) as they work the rodeo circuit.  It's right on I-15

It's a fairground, lots of stalls and arenas. I think it's $10.00 a night

I've also used the Fairgrounds in Laramie Wyoming.  Again right along side the I-80 freeway.

Both of these are public facilities, So they probably don't get the cleaning attention that some private Horse motels get. But they usually have 100-200 stalls so you can find one that is clean.

Also look at http://www.horsemotel.com/

I used them when I moved my horses from CA to TN in 2003.  Every stop treated my back yard trail horses like they'd just won the Rolex.  Great great folks out across this United States and the care and concern of the horse folks is right at the top

Something else to consider if you haven't already:

http://www.usrider.org/

They are the AAA of the horse world only better.  If you break down, they will not only find a place to do the repairs but they bring water for your horses OR will carry your horses to a place of safety until you can pick them up.

Best $198 I spend every year.  That price gets me, hubby, both our trucks, the horse trailer, and the race car trailer fully covered better than Triple A could ever think of covering us  Or it's $119/yr for one person.

 www.horsetrip.com is another good source of overnight stabling.