If you're in Mainz for more than just a day I recommend to visit Bingen, a small town about 15 minutes by car from Mainz. Its landmark is the so-called 'Mäuseturm' which you can see in the picture. Furthermore there's a really nice castle called 'Burg Klopp'. For more information visit the homepage of Bingen at: http://www.bingen.de
Bingen is about 1 hr by train from Mainz. Easily accessible from Bahnhof .
Recommended to visit the town as the best way to understand the lower rhine culture is to visit the towns outside of the cities.
Nice friendly people there. Great view of the Rhine and some ruins including the castle in the middle of the town.