A used 5770 will for $90-100 in good condition. I'm not certain on framerates for games, but in terms of pure performance when looking for an 80% upgrade @ $100, it's unrealistic. The closest you'll get to that figure with a single GPU is the GTX 580/ATI 5970. I recommend looking at one of the TPU charts.
NVIDIA GeForce GTX 560 Ti 1 GB Review - Page 27/31 | techPowerUp
I would probably go with another 5770 for crossfire, or buy a used 5870 ($200) unless you want the latest generation... regardless though, 5870 > 6870.