I have a database of over 300 aircraft kits, which I searched by price. The manufacturers of the following kits sell them for $3,500 - $5,500 and claim that they can be completed for under $7,000 by resourseful builders.
Airdrome Aeroplanes, Inc. Dream Classic Wire Braced
Better Half VW Legal Eagle
JDT Mini-MAX 1100R Mini-MAX
JDT Mini-MAX 1500R Open Cockpit
I don't know anything about these kits, so I cannot recommend one over another. If you have other criteria (range, gross weight, cruise speed, useful load w/full fuel, interior width, etc.) I'd be happy to run them against the database.
The Kitplanes web site also has an online kit finder. You have to subscribe to their online option, but it's worth the $40.