what can i run with a geforce 6800?

Hello. I am looking for a new monitor, 22" to 24" range. Preferably 22. I plan on building a new system at the end of the summer, but I need a new monitor now. I had this ViewSonic A70 for SEVEN years now, if not eight, and all the colors are really messed up. Anyway, I need a new monitor now. this thing is too big, too hot and i'm tired of it.

Can I run a 22" or 24" monitor, at a decent resolution, using a 128mb card? I
dont plan on playing any FPS games.

Yes you should be fine since you are not playing FPS games.

However, if you play strategy games you may need to stick with slight older ones, or at least ones that do not really stress the video card. Supreme Commander is an example. I recall that when Civilization IV came out it pushed the video card as well.