Begin at the Goethehaus und Goethemuseum, the home of Germany's greatest poet. The house is within a 5- to 10-minute walk of either the Hauptwache or Willy-Brandt-Platz subway station. Next, follow Bethmannstrasse as it turns into Braubachstrasse to reach the Museum für Moderne Kunst, one of Frankfurt's modern architectural monuments. Walk a few blocks and several centuries back in time south to the Kaiserdom. The cathedral is next to the heart of the city, the Römerberg. The medieval square holds the Römer, or city hall. After lunch, cross over the Main on the Eiserner Steg to reach the Städelsches Kunstinstitut und Städtische Galerie, with its important collection of old master and impressionist paintings, and the Städtische Galerie Liebieghaus, which contains sculpture from the third millennium BC up to the modern age. In the evening, relax in one of Sachsenhausen's apple-cider taverns.
Spend your first morning at the Goethehaus und Goethemuseum and Römerberg Square, with the Römer, Alte Nikolaikirche, Historisches Museum, Paulskirche, and the Kaiserdom all nearby. After viewing the cathedral, continue up Domstrasse to the Museum für Moderne Kunst. Take a midday break before continuing north to Germany's shop-'til-you-drop Zeil district and the Zoologischer Garten, one of Europe's best zoos. End the evening listening to music in the Frankfurter Jazzkeller. The entire second day can be devoted to the Sachsenhausen museums, starting with the Städelsches Kunstinstitut und Städtische Galerie and the Städtische Galerie Liebieghaus. Finally, explore Sachsenhausen's nightlife.
Spend your first two days following the itinerary outlined above. On the morning of the third day, see the Naturkundemuseum Senckenberg it has a famous collection of dinosaurs and giant whales. Afterward visit the nearby Palmengarten und Botanischer Garten, which have climatic zones from tropical to sub-Antarctic and a dazzling range of orchids. Take the U-bahn to Opernplatz, and emerge before the 19th-century splendor of the Alte Oper; lunch on Fressgasse is not far away. In the afternoon, go to the visitor's gallery of the Börse to feel the pulse of Europe's banking capital. Then continue on to the less-worldly Karmeliterkloster. Secularized in 1803, the monastery and buildings house the Archaeologisches Museum. Just around the corner on the bank of the Main, in the former Rothschild Palais, the Jüdisches Museum tells the 1,000-year story of Frankfurt's Jewish quarter and its end in the Holocaust.