I can help you with Frankfurt...
Somebody mentioned the Frankfurt walking tour. This is a fantastic way to learn about Frankfurt and you will undoubtedly see places and things that you would otherwise have missed. Your tour guide will also be able to give you a few tips about where to go and what to eat.
www.frankfurtonfoot.com
You are too early for the Christmas markets. Almost. There's one on top of a multi-storey car park just off the main shopping street (the "Zeil"). It's already open and the views are amazing.
Try a red or white Glühwein (mulled wine) or a Feuerzangenbowle. Be careful with that one. It's strong!
If you're around on Thursday (9 till 8) or Saturday (9 till 5), go to the Konstablerwache farmer's market. That's at the top of the Zeil. It's a brilliant place to people watch. Also to drink good local wine, a great beer, or to try one of the other local specialities...
Apfelwein: Like a non-fizzy, acidic scrumpy cider. Hugely beloved in the Frankfurt area. Drunk "pur" (as is), "sauer" (mixed with fizzy water, pronounced very like "sour") or "suß" (mixed with Fanta. Not ordered by locals). I strongly recommend trying "sauer".
Handkäs' mit Musik: A sour milk cheese. Quite string tasting. Usually served with a dressing of oil, vinegar, caraway seeds and raw onions. These last provide the "Musik" later on. As farts.
Kartoffelpuffer: Deep fried potato pancake. (Batter contains milk - these aren't pure potato) often served with "Apfelmus" (apple puree) or Frankfurter Grüne Soße.
Grüne Soße: Literally green sauce. A cold sauce made from 7 fresh herbs and sour cream. Traditionally served with boiled potatoes and hard boiled eggs. Also great on a schnitzel.
Schweinehaxe: Pork knuckle. Should be huge and covered with amazing crackling. Some are better than others. Usually served with mashed potato and Sauerkraut. Huge food.
Check out Alt-Bornheim or Sachsenhausen for traditional Apfelwein pubs with traditional German food. (Lots of pig. Also Sauerkraut)
And if you like museums and art galleries, Frankfurt has some wonderful ones. They're mostly along the south bank of the river. Unfortunately they're not free entry though.
I think that'll do for now, but feel free to PM me. I'll be travelling, but I'll try to get back to you.
Frankfurt gets a bit of a bad rep, but I love this city!