Being a Navy wife, I think he went abroad because of all the US civilians and military that live in Europe.
In which case he could have requested access to the military facilities in Europe (which would have been granted), given a speech at Rhein Mein, Landstuhl, Heidelberg, Germany or Rota in Spain, or all of the above, and went home.

Instead, he asked to use the Brandenburg Gate, which would have been loaded with symbolism.

His speeches were squarely aimed at the population of Europe, not US military personnel living abroad.