Interesting places to stand:
Site of the former Bornholmer Straße Checkpoint at the Bösebrücke -- the first checkpoint to open on Nov 9, 1989 as part of what was truly an "accidental" opening of the Berlin Wall when the head guard tired of holding back the chanting East Berlin throngs with no guidance from his superiors, so... he opened the gate to let people pass into West Berlin. Sadly, the checkpoint building is gone (replaced by a Lidl, as all good things in Germany are). There is still part of the wall there, and last time I was there, a tiny patch of pavement with faded lane markings from the old checkpoint. There are some boards there with the history of the site (I can't remember if they are in English or just German).
Gleis 17 aka Track 17 at the Berlin-Grunewald S station -- the site where Berlin's Jews were placed on trains for transport to death camps. There are metal grates along the no-longer operating track -- one grate for each transport train and each grate lists the train, destination, and number of souls on board.
Over any Stolperstein (stumbling block) -- brass-colored squares in the sidewalks outside buildings that commemorate the murdered Jews who lived there.
Tempelhof Airport -- one of the primary locations of the Berlin Airlift, one of the USA's greatest moments. Tours of the airport in English were given pre-COVID and are pretty great for those who have interest in airplanes/airports. There is a memorial near the airport to the airmen who died during the Airlift. I left a flower.
Fernsehturm. I think it's pretty cool to stand outside looking up and to stand inside looking down. I've eaten dinner there twice, reserving a table by the window a little before sundown so I can make a revolution during sunlight, during dusk, and during the dark of night. Eat slowly. And get dessert.
I know you said you are not interested, but... the Reichstag. Totally different viewpoint from the Fernsehturm. I've also done the cupola twice -- both times close to sunset. Do the short audio tour while it's still light and then wait for darkness to descend for some really nice views of the city.
Volkspark Friedrichshain -- few places are better to watch Berliners being Berliners. A HUGE park with fountains (including a very cool fairy tale fountain), walkways, playgrounds, sports courts, a random memorial (Polish Anti-fascist fighters, as I recall), two hills made out of WWII building debris.
Tiergarten -- nice for a walk, especially Luiseninsel; there is an outdoor cafe/restaurant this is a nice place to people watch
The Soviet War Memorial at Treptower Park is stunning and well worth a visit. It includes an enormous statue of a Soviet soldier crushing a swastika with his foot while holding a German child. It is built atop a mass grave of Soviet soldiers. Treptower Park is nice for a walk, too.
Rathaus Schöneberg. Ich bin ein Berliner. And exactly zero people in the crowd chuckled, thinking he was erroneously talking about jelly doughnuts. The inside of the building where JFK gave his speech looks like it is still trapped in the 1960s. I went to the men's room and wondered if there was any chance I was peeing where JFK peed. If you ask really, really nicely, the guards at the front desk may let you go up to the bell tower to see the Freedom Bell; it was a gift from US citizens, who each made a small donation to have the bell cast for West Berlin. It arrived in 1950.
Near MOLECULE MAN! I love that guy. I don't know why.