I am still looking into a new computer. My dad got me a paper with something he think i might like.
It says its an HP Pavillion Desktop
$789.99
AMD FX-6100 Six-Core Processor with Radeon HD 7450 Graphics.
Feature 1GB DDR3 dedicated and up to 4855MB total video memory for lush images and stunning detail.
How well can this run Skyrim?

I think it should run Skyrim
I think it should run Skyrim on high settings. My buddy has a Samsung laptop which has a video card with 1GB GDDR3 (I don't know the CPU, probably an AMD of some sort) but he says he can max it out.
Yeah, I'm also in the same boat. I'm going to be building me a hackintosh this summer so I can do some serious modding.
But getting back to your question, I think it should run Skyrim on high settings fairly easily.