Currently I've got an Intel Q6600 Core2 Quad @ 2.66GHz along with a Radeon 6670 w/ 1GB GDDR5. It runs Skyrim between 30 and 60 fps. I'm wondering if anyone here has a similar CPU with a Radeon 6770 and can tell me... does it run Skyrim at 60 fps constant? I have a small case and the better cards seem to be larger in size so a 6770 seems like a good upgrade option.

The 6770 is actually the same as a 5770 (they just changed the model number) -- which is what I have and it depends on the size monitor you are using -- for 1920x1080 it does struggle at times to keep decent frame rates but overall is decent performance as long as you do not get crazy on the settings and effects.

If I was buying currently though I'd go for something just a bit better as the 128 bit memory interface does limit the performance as you increase resolution and AA etc. --- and for just a few $ more you can get say a 6790 which has the 256 bit memory bus or a 6850(70) depending on your budget as they are all around the same $120 - $160 range and worth the small amount more for the better performance level.

I second JDFan's advice.

I run mine on a 6670, and I get about 30 fps outdoors after tweaking down the settings from ultra(the game defaults to Ultra for some reason). I get between 45 - 60 fps in caves/dungeons, etc..........

Here is a really nice one of the types that JD mentioned in stock: http://www.newegg.com/Product/Product.aspx?Item=N82E16814161363
This one is a bit cheaper and this brand has lifetime limited warranty: http://www.newegg.com/Product/Product.aspx?Item=N82E16814150515

I have a 6770 with 2GB in my new a laptop. It's not the same as the desktop version (stupid confusing names) since it has a 8/24/480 configuration. At 1366x768 (the laptop resolution) Skyrim runs beautifully with aa 4x and af 16x, detail to the max (except shadows). Framerate is steady solid.

I do indeed have an HIS Radeon HD 6770 1GB and it runs skyrim pretty well, although I only have a 3Ghz dual core it still runs up to 60fps most of the time on max settings, hd texture pack included. I only drop down to about 40fps in some towns like solitude but for the most part its been really good ever since the last few patches which have really improved performance on pc.

My old 5770 only struggles if I put shadows on very high. Other than that, it runs the game perfectly smooth with 2xAA / 4xAF @ 1080p.

I ended up going with a 6850 that would fit in my case. Can't wait to try it out. Thanks for the input guys.

No problem link which one you went with I am curious....also just a tip stay away from driver versions 12.2 and above for now.
Here is a link(below) to the driver version I recommend using until they make a better one in 12.4 etc. Enjoy your card and stop back with any questions down the road if need be. http://support.amd.com/us/gpudownload/windows/previous/12/Pages/radeon.aspx?os=Windows%20Vista%20-%2064-Bit%20Edition&rev=12.1