Laptop -

http://www.currys.co.uk/gbuk/computing/laptops/laptops/hp-pavilion-15-p158sa-15-6-touchscreen-laptop-silver-10075691-pdt.html#cat-0

How well would it run Skyrim?

By how well do you mean Vanilla without the HD DLC or modded heavily with a lot of graphics and enb.

It likely will run Vanilla without the HD DLC quite well, I would say medium or high settings depending on the resolution. ENB Boost might or might not help. You get more bang for your money if you buy a desktop computer.