I'd also suggest to go to Mainz or Wiesbaden though shops will be closed on Sunday. (The weather forecast predicts bad weather).
FRA has a website
www.frankfurt-airport.de in english.
Copied from the site:
Airport Tours: Take a Discovery Tour!
Do you want to get a close-up view of the airport and be closer to operations than the air traffic controllers in the tower? If yes, you will certainly be interested in one of our bus tours / tours or other events. Our staff speaks several languages and will gladly tell you everything about how this airport handles aircraft, 1,200 takeoffs or landings and 150,000 passengers each day.
Have lots of fun on your discovery tour!
Important information on visitors' services!
Individual Tour
You get on the bus and drive across the apron of the airport. While on the bus you get a close-up look at airport operations. Furthermore, you get an inside look at the terminals, cargo area, runways.
The airport tour is offered for individuals and small groups of less than 20 persons. The tour lasts approximately 45 minutes. The tour starts at the cashier near gate B22 on the visitors' terrace in Terminal 1. At the moment the tour is offered on weekends between 1130 and 1630 hours. Prior booking is not possible.
Since changes are possible, it is recommended to call one day in advance and check the current tour hours.