The only card with a real shot of hitting 30fps or 60fps is the HD 6670. It hits 30fps at 1080p in Dirt 2, Far Cry 2 and H.A.W.X. Additionally, it comes close in F1 2010 and Just Cause 2, hitting 30fps at 1600x900. With a little bit of tweaking you can hit 30fps in most titles. I didn't go through the work to determine the settings in each game on the HD 6670, but I did find that 30fps is possible on virtually every title using Medium settings with the A8-3850 APU. This utilizes an HD 6550 core, which is far less powerful than the HD 6670.
One thing to note is that almost all of the titles played very smoothly, with minimum frames close to their average. Far Cry 2 had it's jitteriness, and the Heaven Demo was particularly demanding. For everything else I'm confident that the mild bit of tweaking would provide not only an average of 30fps in most titles, but maintain a minimum above 30fps.
These cards aren't going to run away with any performance awards, but they weren't designed to. What they are doing is providing a better experience for the large mainstream segment of the computer-owning populace. I wouldn't recommend an HD 6450 for anyone who plays anything more than Angry Birds or Plants vs. Zombies. Having said that, the HD 6450 is improved over the HD 5450 in that it will actually run all of the tests in our benchmark suite.
The HD 6570 and HD 6670 are decent little cards, and I would always recommend going for as much power as possible. Both cards offer solid performance boosts, and do so with a much smaller power draw and a smaller price tag over their predecessors. If you've got the money for a 1GB HD 6670 it could make a nice foundation for a 2nd PC or HTPC, especially a fan-less version. This is especially true when you consider that it often outperforms the HD 5750 which was never offered in a fan-less versions and required a 6-pin PCI-e power connection.
I haven't yet tested the HD 6770, but it's just a re-branded HD 5770 (which we have in our scores). If you want 30fps/60fps at max settings, I would recommend the HD 6790. What I do think is really interesting to watch is the performance of the HD 6570 and HD 6670, and project how this level of performance will change the computing landscape as it gets rolled into future APU releases.