In a convertible, I would say to get a good late model you need to spend a little more.
For 4 seats, consider a recent BMW 325i, 328i, Mustang, Camaro, or Jeep. Mercedes is also known to make a very nice 4 seat convertible or two.
For two seats and for close to your price range you can get a nice Miata, S2000, Boxster, or Z4.
If you don't mind a project you can really go back and get one of the roadsters that started it all. You can buy a lot of MG, Triumph, Fiat, or Alfa Romeo with 10k. You can get a nice classic Mercedes SL for close to 10k, and the Karman Ghia is around that range as well for a later year driver.