You can get a decent 2000ish r6 for under 4 grand now days. I remember when I was looking around, I saw lots of r6's going for 4-5 grand, but my price range was only 2-3 grand.
For that price, you should find a decent shape 2001+ gsxr600. My friend has an 03 gsxr600 with 6500 miles for 5 grand and it was in perfect shape minus a scratch or two. And since it is winter, prices should be a whole lot cheaper. I've actually seen some 2003-2004 CBR600RR's for 5-6 grand in my area.