AH still runs on my 6800GT pretty nicely. You might be able to find one on ebay or craigslist for not very much money, and it should be a bit faster than your old 6600. With some attention to the detail sliders, I'm able to run 2xQ or 4x antialiasing at 1280x1024, which makes the image quite a bit nicer.
I can't recommend anything newer since I don't have any current info on AGP standards... You might be able to find a 7800 for not much more than the 6800 and it might be compatible with your mobo. I tried a 7800 of some sort on my mobo though, and it was completely unstable. I don't know if that was due to the mobo, a bad card, or maybe even a bad PSU, because I returned the video card instead of having it replaced under warranty. The 6800GT is "good enough" and upgrading it isn't worth the hassle at this point.
Of course, my eventual plan is to do a complete system upgrade and buy a current-generation video card. I know AH doesn't need all that power especially at 1280x1024, but I'll be able to turn up antialiasing to extreme levels to help get rid of the jaggies and shimmering that I find especially irritating in flightsims.