$700 is pretty tight. If you could just sacrifice another $100, then you can get the very popular Dell Inspiron 15 or Acer VX 15. Those boast pretty good specs, and hence also ample 1080p gaming performance.
As for $700 dollars, you will most likely be dealing with integrated graphics. I don't know what company you prefer but you can try the Dell XPS 13 base model or something from Lenovo.