Buying a pre-built will not get you there. You're gonna have to build it to play 1080p on medium for around that price.
PCPartPicker part list:
http://pcpartpicker.com/p/mW9F
Price breakdown by merchant: http://pcpartpicker.com/p/mW9F/by_merchant/
Benchmarks: http://pcpartpicker.com/p/mW9F/benchmarks/
CPU: Intel Core i3-3220 3.3GHz Dual-Core Processor ($119.99 @ Amazon)
Motherboard: ASRock H77M Micro ATX LGA1155 Motherboard ($69.99 @ Newegg)
Memory: Corsair Vengeance 8GB (2 x 4GB) DDR3-1600 Memory ($35.99 @ Amazon)
Storage: Samsung Spinpoint M7E 320GB 2.5" 5400RPM Internal Hard Drive ($59.99 @ Newegg)
Video Card: XFX Radeon HD 7870 2GB Video Card ($229.98 @ NCIX US)
Case: NZXT Phantom 410 (White) ATX Mid Tower Case ($99.99 @ Amazon)
Power Supply: Antec Basiq Plus 550W 80 PLUS Certified ATX12V Power Supply ($54.99 @ Newegg)
Optical Drive: Lite-On iHAS124-04 DVD/CD Writer ($17.99 @ Newegg)
Total: $688.91
(Prices include shipping, taxes, and discounts when available.)
Change the case for a cheaper one if you want, or change it to a CM ATX case for good airflow. If you do change it, you could add the money somewhere else like the cpu or something.