Introduction 

Frankfurt, being the 5th largest city in Germany, has a large variety of cultural attractions. There are dozens of museums in the city. Numerous artists and musicians live in the city. The opera house in Frankfurt is one of the best in Europe, and the theater district is fantastic and well known throughout the world. The opera house and the theaters put on some terrific performances all throughout the year. It is usually hard to get tickets but if you try hard you can find tickets. In addition, the landscape and attractions of the city present a highly-refined culture that embraces all schools of thought and adopts a progressive attitude. If you are traveling throughout Europe, or just Germany, you must head to Frankfurt. There are tons of things to do, including numerous art galleries and outings that encourage intellectual development.

Theaters/Opera

 For English speakers, here a couple of highly recommendable options:

The English Theater (in the city center) - fantastic plays and musicals from Broadway, London or other Anglophile countries. The largest English speaking theater on the continent.

The Oper Frankfurt - Classic opera pieces (Tosca, Fledermaus, etc.) are played and adored on a regular basis

The Alte Oper - they get all the big acts, Buena Vista Social Club, River Dance, Symphony Orchestras, and so on

The Mousonturm (in Bornheim) gets terrific live music venues

Theatre Language Studio Frankfurt offers terrific English language theatre productions, such as their monthly improvisation comedy troupe Frankfurt International Theatre Sports, which has late-night shows the first Saturday of every month in Bornheim. They also do a unqiue four-person rendition of A Christmas Carol every year at Haus Sindlingen called Dickens by Candlelight.

For German speakers, the Schauspielfrankfurt (modern plays), the Komödie (classical comedies), the Stahlburgtheater (cabaret), the Käs (satire) and the Schmiere (satire) are standard bearers in their respective fields

Museums

There is a wealth of museums in Frankfurt that for its relatively small size, is simply astounding. For starters, here are the five standouts, so you don't get lost in the rock 'n' roll:

1) The Staedel, if you only have time for one museum go see this one. It's Frankfurt's "Louvre" and often has amazing special exhibtions

2) The Judengasse and Jewish Museum, presenting the long and rich history of the Jewish Community in Frankfurt.

3) The Schirn Kunsthalle, this more modern exhibition museum has all the contemporary and modern artists and doesn't have a permanent collection. Thus, it is always a (mostly positive) suprise what awaits you here.

4) The Museum für Moderne Kunst (MMK), puts its emphasis squarely on modern art. Joseph Beuys, Warhol and Liechtenstein are only some of the names.

5) The Deutsches Architekturmuseum along the Main River has some of the best exhibitions in Frankfurt and shows why architecture plays such a big role in this city (almost like no other in Europe).

Other  worthwhile museums include the the Giersch Haus (Regional paintings and Regional artists), the sculpture museum Liebighaus, and the Museum der Weltkulturen, all located beautifully along the Main river. The Archeology Museum with the history of the Celts, Romans and Franks in Frankfurt, the Historic Museum with lots of medieval art and a scale model of the Alt Stadt of Frankfurt,  the Communication Museum, the Icon Museum, the Dialog Museum, and the Leather Museum in Offenbach.

Conclusion

Cultural boredom is hard to come by in Frankfurt.