I will assume that you don't want to do everything within this year's 12-14 days trip. Otherwise it doesn't really make much sense.
First some general hints:
- Frankfurt has Germany's largest airport, so it is easiest to reach as all major carriers will have direct connections to FRA.
- Munich has Germany's 2nd biggest airports, so your chances of getting there by direct connection are pretty high.
- With the new airport opening this year, Berlin will be far easier to reach than in the past, especially if you want a direct connection from the United States.
- Nuremberg has one of the smaller airports in Germany, so you will have a stopover, same goes for Cologne.
Since you don't want to drive and want to see much, I would definitely advise on using trains. This is by far the most time-efficient (and probably money-efficient) thing to do. You might want to look into the various discount options for German rail. A BahnCard 25 (giving you 25% discount on all train tickets for EUR59) would be a sure bet for you.
As for the itinerary and your mention of Cologne:
Yes, Cologne is nice and certainly worth a visit, but if you start from Berlin, there's no easy route to include it except by flying there from Berlin or Munich, but since you want to avoid domestic flights, may I suggest that you include Cologne in one of your next trips and then choose a more western itinerary including Bonn, Koblenz, Bingen, Mainz, Heidelberg and so forth.
The mentioned itinerary of Berlin-Dresden-Leipzig-Bamberg-Nuremberg-Munich-Salzburg has the advantage of relatively short train rides (never more than 2-3 hours), which enables you to see more of the different cities.
However let me add to one of your last post, that there are far better christmas markets than Berlin has to offer. Also depending on where you arrive, it might make sense to add Frankfurt and Mainz to your itinerary as both have very nice christmas markets in their respective oldtown quarters.