Restaurants do a booming business on Sundays!
If you would like to try a typical Frankfurt meal, head over to Alt Sachsenhausen and have the Frankfurt Green Sauce on potatoes or a Frankfurt Schnitzel. Try Dauth-Schneiders, or Lorsbacher Thal. For dessert, try a Frankfurter Kranz.
There are. few small Christmas markets open already. One is on top of the parking garage near the Konstablerwache, another one is about 1 block off of the Zeil if you walk down Hasengasse past the Kleinmarkthalle, and a tiny one is at the end of the Eisener Steg bridge. They are only doing food and drinks, but still fun. They will open around 1400 or 1600.
The Kleinmarkthalle is open on Sat. until 1600 and they have a nice wine and grill party outside of it on Saturdays. There is also a large Farmers market on Sat. on the Konstablerwache. Open until 1700.
Not sure which museums you are going to, but my recommendations are the Judengasse Museum, the Städel, the Film Museum, the Liebieg Haus, and the Jewish Museum.
Almost all of the museums are closed on Mondays.