look at Craiglist (if your city is large enough to be listed) for rentals, most state right in the ad if dogs are allowed. Some ads have pictures of the places, too.

I rented with a dog before Craigslist and other internet resources and it took a lot of time on the phone to find a place that would take a dog. It was hard, and I ended up taking a 2 bedroom place (more expensive and more 'generic' than some of the beautiful historic places I looked at), but I had a plce for all my cats and my dog.