We bought my daughter a Lenovo IdeaPad Y570 which she likes quite a lot. It's no longer available, but its
successor is. It's selling for $800 today after an alleged $500 discount.
She plays the same games you're interested in --
Skyrim and
Dragon Age in particular -- and says they work well on this machine when the NVIDIA adapter is activated.
After some bad experience with an HP laptop, I would never buy one of them again.
I've had pretty good experiences with Dells over the years as well. Dell only ships ATI graphics these days; I prefer NVIDIA which gave the Lenovo an edge in my book.