If you are on a budget, then the following 15.6" Acer laptop with a Core i5-5200u, nVidia 940m and 1080p screen is selling for $490.
http://www.newegg.com/Product/Product.aspx?Item=N82E16834315131&cm_re=acer_940m-_-34-315-131-_-Product
It should be decent enough to play FO4 on mostly medium settings at 1600x900 resolution. But you will need to disable anti-aliasing and set shadow quality to low. Special effects like Godrays should be disabled.
If you can afford $800, then the following Dell Inspiron 7559 has a quad core i5-6300HQ, nVidia 960m and 1080p screen. You should be able to play FO4 @ 1080p and high settings.
http://www.amazon.com/Dell-Inspiron-i7559-763BLK-Full-HD-GeForce/dp/B015PYYDMQ/ref=sr_1_1?ie=UTF8&qid=1450725280&sr=8-1&keywords=dell+inspiron+7559