Landy, Tell me how you determined a need for a non-qualifying home? Most requests are for a certain number of bedrooms or baths within a pre-approved price range given once you have met with a lender. Expound a little on what your situation is. Most Realtors have experience in working with all types of purchasing scenarios.
The zip codes you mentioned have a wide variety of properties that would make wonderful homes so don't be afraid to ask for help.