Russ, as always, gives excellent advice. I agree with what he said in both posts, so I won't rehash.
Since teenagers are involved (I'm assuming US teens), I will offer a couple of ideas for Berlin that may be of interest...
In my mind, one of the US's finest moments is the Berlin Airlift, when the US (along with the Brits) supplied West Berlin by air after the Soviets closed all ground routes to the city in June 1948. If you land at Tegel, you will be at an airport that was created to support the Airlift. Tempelhof Airport, a now-decommissioned airport in the city, was the main airport in Berlin in 1948 and was also used extensively. English tours of Tempelhof are available and in my estimation, the airport is well worth a visit. There is a memorial to the Airlift and the people who lost their lives during it outside the airport; you'll see flowers on the memorial to honor them. If your sons are not familiar with the story of Gail Halvorsen, who became known as the Candy Bomber, it's a worthwhile tale for them to know before arriving in Berlin. The full 41-minute PBS documentary about Halvorsen is here and contains a good summary of the Berlin Airlift.
I don't know what your budget is, but if I had sons who were 15 and 17, I would consider hiring Robert Sommer for a few hours for a tour in Berlin (perhaps a Cold War tour?). He was the 15 yo son of a somewhat high-ranking bureaucrat in the DDR (old "East Germany") on the night the Berlin Wall fell. He went on to get a PhD in history and now gives tours in Berlin (among other things he does). During a a tour, he can tell you about growing up in the DDR, his experience the night the Wall fell, and the capitalist product he held out on trying the longest. Open-ended questions free of preconceived notions, of course, will get the best answers; "What was it like growing up in the DDR?" not "I bet it sucked growing up in the DDR"). You also might hear something a little different than the accepted "victor's history" of German reunification. Even though Robert has a PhD, he is very down-to-earth, friendly, and approachable. I much enjoyed my tour with him.
If you are a Dietrich Bonhoeffer fan, I have a recommendation for a site related to him in Berlin, too, if you are interested.
If you would like to eliminate a stop, Esslingen has Rothenburg ob der Tauber charm, but is a 15-minute train ride from the center of Stuttgart. Esslingen's manufacturing area was on the river, away from the town, so the town largely escaped WWII bombs. There are half-timbered houses galore, stunning churches, and city walls that can be walked. Sarah at Stuttgart Steps gives a very reasonably priced tour of the town that incorporates its history into what you see. Sadly, there is no nightwatchman's tour (at least to my knowledge).
Happy planning!