My wife and I love Drury Inns overall and their pet-friendliness in particular -- and we stop at the Drury Inn-Southeast in Birmingham every time we travel through Birmingham. Drury Inns never charge for pets and are easily the most upscale of the hotels that don't charge for pets. The Drury Inn-Southeast Birmingham, like all Drury Inns, offers competitive prices, a super friendly and helpful staff, with great accommodations and superb evening snacks and morning breakfasts. The Drury Inn-Southeast is also nice for dog owners because it's slightly more removed from the interstate, in an office park, and offers many nice views and places to walk a dog. I heartily recommend the Drury Inn-Southeast in Birmngham.
I thought the hotel was clean and courteous; however, you are only allowed to leave your pet unattended in the room for a short period of time. We went to the theater while we were there and had to leave our dog in the car during the performance so as not to break hotel rules. The weather was comfortable for our dog so it wasn't a big deal and as it was night we didn't have to worry about her overheating. It would have been nice to leave her crated in the room, but I do understand that some dogs might bark and disturb other guests.