I am currently using an Acer Aspire F-15 to play FFXIV. I would consider that it runs the game well. This is likely connected to installing FFXIV on its 250GB SSD drive, which improves loading speed of the game. However, the left side of the laptop (which I suspect is where the video card is housed) gets uncomfortably warm when I run FFXIV, which affects my typing on the keyboard. This issue may be circumvented by plugging a USB keyboard to the laptop.

I am unable to ascertain the current price of an Acer Aspire F-15, but you may also consider the comparable Acer Aspire V-15. The Aspire V-15 specs more than meet FFXIV minimum specs and is currently being sold on Amazon at USD 729.