I was doing some searching, too, for our trip from San Diego to Michigan and back. Staying in NE and NM.

I joined the AAA online membership thing (w/ my boyfriend's actual membership info) and got hotels for prices in our range. Then I just clicked on the ones showed AAA discounts and looked for a "pets welcome" icon. Then, I looked
at those hotel websites for more info. Some charged a fee, or small pets only, or pets OK in specific rooms , etc.
I know Super 8 (the one we're staying at charges $0 and no other restrictions... so they tell me...) and Motel 6 take them but I don't recall if there's a fee.
We are staying at a Travelodge that accepts pets, too, for a $10 fee w/ no other restrictions. And with the AAA discount it seems worth it.

ANYWAY - that was a lot of rambling mostly cuz I'm bored...
Sorry.

Good luck however you do it!