Does the $650 budget include a monitor?
If not you can get a HP p6370t desktop computer
with a Core i3 530 2.93Ghz CPU, 4GB RAM, 640GB HDD and an upgrade HD 4350 512MB video card for about $600 from the HP store. Should handle WoW very nicely, along with having plenty of power for other computer tasks and all but the most graphically demanding games.
For help in figuring out what your $650 will get you in a home build check out the THG Homebuilt Systems Forum