There are options avaialble for you in that price range and those zip codes. I did a search and came across soem properties that meet your criteria. A lot of whether you can have the dog or not is going to be based on the type of dog you have. Homeowners are afraid for the liability that is involved when you have animals and they are not willing to take on that liability.....
All of the rentals are going to be contingent in regards to pets based on the type and size of the dog you have.... if you would like to e-mail me or give em a call at 704-519-7895; I would be happy to discuss the options avaialble to you out there right now in those areas and your dog and see if we can find a match for you.