Backup your current Tableau Server, saving the backup to a temp location (for example, C:\temp).
Install Server on your new location.
Restore your above backup to the new location.
When you say backup the Tableau Server, do you mean just doing a simple .zip archive with the TS files, or is this some kind of backup feature within Tableau Server itself? (I'm new to TS)
Further, it appears that the TS software itself is installed at C:\Program Files\Tableau, whereas the big folder that takes up most of the disk space is at C:\ProgramData\Tableau - which one do you mean to restore?
Backup feature. You're going to need to read the Administrator's Guide:
Here's more on backing up your Server, definitely read this: