Sun Dial Estates area usually has exactly what your looking for. I'm in a 3/2 one car duplex with fenced backyard, about 15-20 min to Whiting. $800/mo about 1200 sq ft. Allows pets.
There is at least one duplex and two single family houses on my street that are either for sale or rent.
Check out Pensacolamls.com We looked there and went to check out the places we liked before contacting the property managers.