Here's one way. I don't know if it's the easiest, but it'll work. I don't know what operating system your using either. I have Windows 7. Open the start menu in the bottom left corner. Click on whatever user who's favs you want to save. Click on Favorites and then control select the ones you want, then burn to disk.
Easy way is to send yourself an email from the loaner computer..... copy and paste all the addresses you want to keep and put them in the email.......when you are on your computer open the sites and save them to your favs