In the summer, a walk along the river Main is a nice thing to do. A lot of people will spend a sunny afternoon walking or sitting there on a lawn or playing frisbee or soccer. It's a relatively quiet area, considering it's in the heart of the city. Nearby cafes and restaurants allow you to have a drink in between. The only disadvantage is that it can be quite crowded when the weather is nice; try going during business hours on a weekday unless you're looking for a crowd.
Oper Frankfurt (Opera) - not to be confused with the historic Alte Oper building, this modern building is where to go to see an opera performance. State subsidized performances make this a relatively affordable place to see high quality productions
Go for a walk in the City Forest (Stadtwald) in the south of Frankfurt. With about 48 square kilometres, it is regarded as the largest inner-city forest in Germany. Six playgrounds and nine ponds make the forest a popular tourist attraction. The forest can be reached via tram line 14 direction Neu-Isenburg/Stadtgrenze from Frankfurt South Station (Frankfurt Süd). Trams 12, 19, 20 and 21 also connect the Stadtwald with downtown Frankfurt.
Try the local cider "Apfelwein", especially that made by Possmann. The "Frau Rauscher" edition has a pleasant natural taste with some yeast left into it.
The Saalburg is an old Roman fort just outside Frankfurt, near Bad Homburg. You can either take a bus from Bad Homburg, or take the "Taunusbahn" to station "Saalburg" and walk 45 minutes along the Limes to reach the restored fort.
The Cinestar Metropolis cinema shows a couple of movies in English. Take U1/U2/U3 to Eschenheimer Tor or walk from the city centre.
See a play at the English Theatre, which is the largest English-language theatre in continental Europe.
Ice skating at the Eissporthalle.
See a modern ballet performance by The Forsythe Company (William Forsythe)
Jet fighter flight from Frankfurt Hahn Airport, MiGFlug & Adventure GmbH, Badenerstrasse 286, 8004 Zurich, ? +41 44 500 50 10. Jet type is Aero L-39 Albatros. The customer can fly the jet under close watch of the pilot. Ask for dates.  edit
Go swimming at Titus-Thermen or Rebstockbad, which both also have whirlpools and sauna facilities. Or visit any of the other public indoor or outdoor pools in Frankfurt. Some of the bigger complexes outside the city limits include Taunus-Therme in Bad Homburg and Rhein-Main-Therme in Hofheim.
Sportpark Kelkheim is a sports facility complex that features high rope courses, golf (no membership required), indoor climbing and bouldering, squash, and other activities.
While not the most typically German thing to do, there are several bowling facilities in the city.
Go on top of the 200m high Maintower and enjoy the view over the city and the surrounding region. Entry costs 5?. Closed during bad weather.
Go on top of the Feldberg mountain, the highest mountain of the Taunus. Take a train from Frankfurt central to Königsstein and then go to the main bus place (Parkstraße). Busses via Feldberg depart every 2 hours. Get on top of the observation tower at the Feldberg. If it's cold, have a hot chocolate with cream (Heiße Schokolade mit Sahne) at the tower's kiosk.
Art galleries are spread out in different parts of the city. Some of them are concentrated near the Museum of Modern Art (MMK) in and around the Braubachstraße and Fahrgasse.
The red light district with large brothels, porn cinemas and bars is located just east of the main railway station.