I will be using the "Quote" feature in an unorthodox way throughout this post. My goal is to make this post as convenient to you, the reader and IT Elite, as possible. If it is annoying, my deepest apologies. Consider it my best effort to roll the red carpet out for you kings of men, whom I owe the deepest thanks for your knowledge.
APPROXIMATE PURCHASE DATE:
$100 However, the price of graphics cards should not affect your recommendation. For simplicity, just consider $100 to be my optimistic maximum.
If I understand correctly, the card must only meet the PCIe 2.0 x 16 requirement.
Only in the rare circumstance that an overclocked card is what best meets my needs.
SLI OR CROSSFIRE:
If the graphics card you recommend has SLI or CrossFire support, great! Perhaps I'll take advantage of it when I choose my next motherboard. Otherwise I don't give a damn about either.
The card MUST run The Elder Scrolls V: Skyrim sufficiently to be viable at all. Although I require no specific settings, the game must maintain a decent frame rate. A bonus, VERY BIG BONUS, would be the ability to, decently, run Star Wars: The Old Republic, however, again, no specific settings required.
Your PC only has a 220w PSU which severely limits your choice of video card to the most basic models. Additionally, your PC is a "slimline" model case which limits you to a low-profile graphics card instead of a normal full height card. I'm guessing it uses a mini ITX power supply which means probably the highest output model you can buy is 400w.
Since you only have a 220w PSU, the best graphics card that you can install is the Radeon HD 6450. That is not exactly a "gaming card". See following for benchmarks:
Skyrim is pretty much dependent on both the CPU and graphics card. I assume you only have some type of dual core Athlon X2 CPU. Couple that with a Radeon HD 6450 and you are probably limited to 1024x768 resolution and low graphic settings to get decent frame rates in Skyrim.