It is difficult finding properties in the area that allow pets, particularly in that price range. Fewer and fewer landlords seem to be allowing them, but that will change with the rental market, when landlords are having difficulty finding new tenants, you will see prices drop and more pet-friendly places.
That being said, at the $450 / range that allow pets, your best bet is finding a "room for rent" / roommate situation. I would check Craigslist. Be aware that there are quite a few scams in the rental sections of that website. Don't send anyone any money until you have a signed document and you have seen the unit in person. You may even want to be more proactive and posting your own ad in the local papers and on Craigslist seeking a room to rent that allows for a pet. Good luck!... more