There is a trick to making the transition to a new PC easier than having to set up Google Authenticator from scratch. However, you need to do this during the initial setup.
When you're given QR codes for each site, print them or screenshot them to save them for later. Make sure you name each code so that you know which sites they belong to. Then, if you need to set up a new PC to use Google Authenticator, you just need to install your chosen app from the above list and add in your QR codes. It's quicker and doesn't involve having to remove 2FA from any accounts.