- Copy the base game folder to the new PC
- Copy user specific data from your C:\Users\YourUserName\Elder Scrolls Online\live to the same folder on your new PC
- On the new PC, locate the launcher exe in the base game folder and start it manually
- Select "Repair" in the launcher and it should go ahead and set everything up for you without having to re-download the whole game again
I haven't done this in quite some time, it used to work just fine like that but it may not anymore.