La Quinta Inn Lexington

The rooms are a little dated, but it welcomes pets with no restrictions.
There's a Cracker Barrel across the parking lot that does take out!
There's little grass around the hotel but in the next parking lot over, there are a few islands with grass. Okay for my little pugs but may be a challenge for larger dogs.
Trashcans at every entrance so no need to carry the full poop bags into your room.

Plus, on the same exit but other side of the interstate, there's an enormous dog park (Coldstream Dog Park) to let your guys burn off some energy before or after travel.