Depending on the size and specs you want, your budget would fit a very large catalogue of computers.
Based on previous experience, I would recommend you check out the ASUS G series laptops :
Laptops / Notebooks - Business & Gaming Laptops at Memory Express
Running the latest mobile intel processors and graphics cards, they will handle BF3 in high without much problem, and still fit within your budget (before tax).
Comparable models from MSI also offer much of the same bang for buck. The MSI backlit keyboards are also quite nice.