What to see in Frankfurt

Museums
Museums in Germany are generally closed on Mondays (there are exceptions); the exact opening hours on other days depend on the museum. If you want to visit a museum on a public holiday, check with them before to be sure they open on that day.

The museums in Frankfurt offer a wide range of exhibits. Many museums are clustered on the south bank of the Main in a district called Museumsufer. To get there, take the subway to Schweizer Platz, then walk towards the Main river. You can see the downtown skyscrapers when you leave the station, that's the direction you have to take. There are enough museums in Museumsufer to keep you occupied for a while, and it is especially suitable if you are staying in Frankfurt only for a short time

Frankfurt has some of the tallest buildings in Europe (the Commerzbank tower is the highest office building of Europe), and the tallest in Germany. Its skyline is unique for the country as the high-rises are concentrated in a relatively small downtown area, giving Frankfurt the looks of a metropolis. The skyline is the reason why Frankfurt is sometimes called by the nickname Mainhattan.
For a view of the skyline try the Main river bridges. The eastern bridges offer the best view. Also, when you approach the city from the airport via the subway, stay to the right side of the train. Just before the train approaches the Frankfurt central station it enters a big curve, and from here you will have a nice first glance of the skyline.
Take a walk from Schweizer Platz northwards for another good view of the skyscrapers

Römerberg is a central, old place in downtown Frankfurt. It features various buildings and a church from the 14th and 15th century (in theory; the buildings were mostly destroyed during World War II but completely rebuilt afterwards). The Römer itself is the town hall of Frankfurt. Cafés and shops can be found at the square itself and in the vicinity. A definite tourist attraction. Within walking distance of the Zeil shopping area and the Main river, it is located just north of the Eiserner Steg bridge.

Visit the Old Town and then take a walk across the iron bridge to Sachsenhausen. Here you can walk along the river bank or visit some of the old cider bars in Sachsenhausen.
Do try the local cider "apfelwein", especially that made by Possner.