Actually it is possible to play Skyrim on a laptop within that price range. Out of curiosity, I played Skyrim on my Lenovo Y470 using only the Intel HD 3000 instead of the GT 550m graphics chip. After installing some mods to lower the size of texture and some other manual tweaks to the Skyrim.ini file. Looked kinda crappy, but I managed to level up a new character to level 8 before I decided to end the experiment. That was 2 years ago.
You will not need to buy an old laptop with an Intel HD 3000 graphics core in your price range. The link below is to Bestbuy's Black Friday deals (Nov. 27th - 29th). There are two laptops in your price using current generation Core i3 / i5 CPUs with the Intel HD 4400 graphics core. The HD 4400 is probably about 50% more powerful than the Intel HD 3000.
http
/blackfriday.bestbuy.com/?category=doorbusters2&filter=&sub_cat=Laptops&cat=Computers%20%26%20Tablets
The 15.6" Dell Inspiron is selling for $300 and comes with the Core i3-4030u (1.9GHz) and a 1366x768 resolution screen. The 17.3" HP Pavillion selling for $400 comes with the Core i5-4210u (1.7GHz / 2.7GHz) and a 1600x900 resolution screen. The Core i5-4210 only goes up to 2.5GHz when both cores are used.
Either way Skyrim is playable at 1366x768 resolution without too many tweaks to the graphic settings. You can always search for mods that have lower texture qualities and plays with some of the settings. Here's a link to a short video of Skyrim played with the Intel HD 4400.
https/www.youtube.com/watch?v=vkigD2iErl0
Tomb Raider on the Intel HD 4400
https/www.youtube.com/watch?v=tQp8rEYuXss
Planetside 2 on Intel HD 4400
https/www.youtube.com/watch?v=zLCMB1lA9Mo
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