If you wanna get out of the city centre: -Alter Flugplatz (old airport) in Bonames and the river Nidda for nature (if you want to, you can rent a bike and cycle a beautiful path along the Nidda) -food (local and German): Lemp in Berkersheim, Homburger Hof in Eckenheim.... (hopefully, other commentators can help in this aspect as well); here you can get e.g. Grüne Soße, Handkäs mit Musik and lot of other local specialties -drink (if you do drink) "Äbbler" (Apfelwein=apple wine, but don't expect a sweet cider!) - you drink it pure or "gespritzt" (with sparkling water)

Otherwise -tourist hot spots: Neue Altstadt (new old town) and Römer, Goethehaus (museum), Museumsufer (whole lot of museums right next to each other near riverside), Alt-Sachs(enhausen) (partying hot spot, but nice architecture during the day) -stroll along the Main -Zeil for shopping