http://www.tomshardware.com/reviews/gaming-graphics-card-review,3107-2.html
For $65, it says the best is a Radeon HD 6670 DDR3. It's JUST above your $60 limit at $70 . However, they all come with a $10 or $20 Mail-in Rebate, reducing the cost to $50-$60 sans S&H (which may or may not be free).
Best option: Gigabyte 6670 DDR3 for $70 plus $20 MIR, and free S&H.
Thats what I was looking at, but Might settle on this; http://www.microcenter.com/product/...adeon_HD_6570_2048MB_GDDR3_PCIe_21_Video_Card
Little less powerful, but the extra gb of memory would help out a bunch. Plus it can run BF3 on high at about 30fps, and skyrim isnt as demanding (in most cases)
Her processor is an Athlon II X3 3.2ghz and has 4bg of ddr3 ram