This will play any game on high-ultra settings. It can be overclocked and is really fast. Pretty sure it get 60-80 FPS on ultra settings for skyrim.
EDIT: This is toms hardware review on the 7870 NON GHZ EDITION
http://media.bestofmicro.com/Q/N/328847/original/Skyrim%201920.png , the GHz will have 5 more FPS so its areound 80 FPS on ultra settings for skyrim
PCPartPicker part list:
http://pcpartpicker.com/p/uUvj
Price breakdown by merchant: http://pcpartpicker.com/p/uUvj/by_merchant/
Benchmarks: http://pcpartpicker.com/p/uUvj/benchmarks/
CPU: Intel Core i5-3570K 3.4GHz Quad-Core Processor ($189.99 @ Microcenter)
CPU Cooler: Cooler Master Hyper 212 EVO 82.9 CFM Sleeve Bearing CPU Cooler ($29.98 @ Amazon)
Motherboard: ASRock Z77 Extreme4 ATX LGA1155 Motherboard ($134.98 @ Outlet PC)
Memory: G.Skill Ripjaws X Series 8GB (2 x 4GB) DDR3-1600 Memory ($49.99 @ Newegg)
Storage: Seagate Barracuda 1.5TB 3.5" 7200RPM Internal Hard Drive ($69.99 @ NCIX US)
Storage: Intel 330 Series 180GB 2.5" Solid State Disk ($129.68 @ NCIX US)
Video Card: XFX Radeon HD 7870 GHz Edition 2GB Video Card ($231.98 @ Newegg)
Case: Cooler Master HAF 912 ATX Mid Tower Case ($49.99 @ NCIX US)
Power Supply: Antec High Current Gamer 620W 80 PLUS Bronze Certified ATX12V / EPS12V Power Supply ($69.99 @ NCIX US)
Optical Drive: Lite-On iHAS124-04 DVD/CD Writer ($22.98 @ Newegg)
Total: $979.55
(Prices include shipping, taxes, and discounts when available.)
(Generated by PCPartPicker 2012-12-29 22:06 EST-0500)