A 570 is WAY overkill for 720p.
I have a 5750 (about 3/4 as powerful as a 6850, less than $100 on eBay) and a 1080p monitor, and I can max skyrim except shadows. MW3 and WOW are easier, and SWTOR not much harder. Only BF3 would give you a problem. At 720p (which is roughly half the number of pixels), my card would be able to max every one of those games except perhaps BF3. I'd recommend a 5750, but of course I'll get my throat slit for saying that. A 6850 would also be a great choice, or a 6870 MAX.
If you really want to spend another couple hundred on a 1080p monitor, you'd love life with a 6850 or 6870, even if you couldn't max BF3. It would still look great. If you have cash to burn, a 6950 or 560 Ti (they're roughly equivalent) would be able to max it comfortably. A 570 would naturally be able to max all of them as well.
Do you regularly do any other massively parallel tasks? I render and I wish I had a better card for that specifically... Just something to consider...