I'm looking for a cheap laptop in between $100-$200 that can run CS:GO at an FPS in the high twenties. I'm pretty sure this doesn't exist but it's worth a shot. I only need a little bit of storage for Steam, CS:GO, and some other small things, so storage isn't a problem. The screen doesn't have to be 1920x1080, and I only need about 2 hours worth of battery life while playing.
At bit over your budget @ $220 and it is refurbished, but you are not going to be able to buy a new laptop for $220 that is more powerful than the ThinkPad T440 with a 4th gen Core i5-4200u and integrated Intel HD 4400. Thinkpads are semi-rugged laptops which means they can take a bit of a beating better than most other laptops.
I got Skyrim (not the special edition) to run on a friend's laptop with the same CPU and integrated graphics pretty well with a bit of editing to the SkyrimPref.ini file to lower graphic settings that can't be done within the game's menu. If I can get Skyrim to run around 45+ FPS at 1366x768 resolution, then I am sure it can handle CSGO decently well. However, I recommend you install another stick of 4GB RAM when you have the money. Two sticks of RAM means the RAM runs at full speed rather than half speed. That can generally mean game performance increased by 10% - 15% depending on the game. My friend's laptop already had two 4GB sticks of RAM in it.
Click link below for game benchmarks of the Intel HD 4400 from Notebookcheck.net (scroll down), which includes CSGO.
Are integrated graphics actually able to pull off CS:GO at decent framerates? I was thinking something with an APU would work better but I'm not very knowledgeable when it comes to APUs and integrated graphics.