In that case, I suggest going to Documents\My Games\Final Fantasy XIV - A Realm Reborn

Move the following files to another location, such as the Desktop or a new "Backup" folder:

ffxiv.cfg
MACROSYS.dat
All CHAR_ folders

Then boot up the game again. All settings (HUD, macros, hotbars, system and client settings) will be lost, but if those files were causing the crash it will let you login again. Reinstalling doesn't necessarily affect all these files you see, yet they could be the cause.

If it works, you can slowly drag each file back in one at a time until the crash happens again, rebooting the game between each one. Once it crashes, you will know which file is the culprit.