There are a lot of those type of apartments in the North Main and Stone Avenue area and also near Bob Jones University off of Wade Hampton Blvd and East North Street, both on the Stone Avenue end. A lot of them are usually rented by putting a sign in the yard. I know that is not ideal for someone relocating, but I would suggest staying in an extended stay hotel for a couple of weeks while you are searching. You may also want to check the Iwanna website
Free Local Classified Ads in NC and SC - IWANNA