I suggest you do a search on this forum using the words FRA and Mainz and then decide what is more up your street. There are dozens of threads that cover this subject. I'm not a great fan of Mainz (there's a joke about Mainz which starts "Two prostitutes are talking about Mainz..." but it doesn't really translate very well! Frankfurt is really not that much of a sightseeing town beyond the Altstadt.

If you are feeling adventurous, I would rent a car (or take the train) to Heidelberg (about 45 mins drive). Much nicer.

Welcome to FT!