try
www.rentwithpets.com
or call the local humane society or shelter and ask them for pamphlets or referrals. You should be able to find an apartment rental book of some sort that will help you narrow it down.
I haven't encountered that problem b/c I just looked at apartments and my dad finally said "this is really stupid, you need to find something to buy." and lo and behold we found a TINY house with one bedroom,living room, kitchen, and bathroom and a 2 car garage, that I could afford. Most of my friends that have apartments are appalled at my house payment!!!! $250.00!!!! I moved in in June and my animals came after that!!