For $500, you're pretty much surrounded by 15.6" screens, with either APU or HD3000/4000 graphics.
The laptop I recommend is the Lenovo Z580, an ivy bridge processor @ 2.5Ghz, with HD4000 graphics. I have previous experience with lenovo, so that is a reason as to why I'm suggesting them. The laptop itself seems to be the best one in its category of under $500.http://www.newegg.com/Product/Product.aspx?Item=N82E16834246616&name=Laptops-Notebooks
The laptop will be able to handle every day computing, and HD playback with ease. Even if one wished to throw some light gaming on it, save for graphically intensive games they will be 'playable' with lower settings.