When I travel with my cat, I tend to stay at the Choice Hotel chains because a lot of them are pet-friendly.  Try Quality Inn, Comfort Inn, Econo Lodge, Rodeway Inn and those brands.  Sometimes they aren't the nicest rooms, but your pet is usually welcome. 

I don't travel with my cats often but if I have to I look online for hotels that accept pets and then call them to make sure it's true. 

My son shows Great Danes. They routinely stay in Motel 6 because they allow pets. The rooms aren't that great but he says that they are adequate for him and the dog/s for sleeping.

Timeshares typically don't take pets, but there's one in MA that actually has "pet friendly" buildings.

Actually the higher end hotels are more likely to take pets than those in the mid range. I regularly bring my boys with me to Omni Hotels, Westins and some W hotels. I check the web site and call to confirm. Often you have to pay a non refundable pet fee but then they are welcomed. The W line of hotels even has dog food on the room service menu.