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Try searching Apartments.com. You can filter by number of rooms and short term leases. You can't filter by flooring type, but you can do a keyword search like "hardwood".
More than likely though, even if you find a place with wood floors, it'll probably have carpeted bedrooms. Most management companies will have carpets cleaned in between tenants. Or you could have them cleaned yourself.
Another possibility is to look for a sublet from someone in the academic community (Duke, UNC, NCSU, etc)...faculty on short sabbatical, for example. There are rental/sublet listservs for these campuses if you can find someone with access.