Ok, here's a more detailed account of yesterday.
I got going from the hotel moderately late and arrived at Alexanderplatz ~10.15 where a queue was aready forming for the viewing platform on the TV Tower; I'm pretty sure I waited longer at the Empire State building, though. Just over 200 m up and extensive views over Berlin and the surrounding area. Photos aplenty but I'm not very hopeful - pics through glass often don't work well.
After that I wandered over to Berliner Rathaus, then Nikolaikirche which claims to be the oldest building in Berlin and has very photogenic twin spires and on to Berliner Dom, which I bought a ticket for. A service was in progress. I always feel uncomfortable being a tourist in a place of worship when actual worship is going on, so I was glad to get going up the stairs out of sight and no longer be a possible cause of disturbance.
There's several "attractions" - seems like not quite the right word - including the crypt, a balcony allowing a view up to the spectacular main dome and down to the floor of the church and a museum area that incudes several scale models of church buildings. The best part is the "Dome Walk", though, especially the outside part. Photo-blitz!
After that it was time to go back to Wittenburgplatz, have a last currywurst mit pomme frites, bitte and get a taxi to the airport. Bye-bye, Berlin! It was tremendous, exhausting fun.
A few bonus experiences:
A couple of people shooting a bad video to a bad song on the steps of the Alte National Museum; a woman doing a handstand in front of a side entrance to Marienkirche while her friend photographed her; four teen girls formation dancing badly to a worse pop song they were playing in Alexanderplatz.
People = weird!