The best way to get a good overall impression of Berlin is to go on a bus or a boat tour. We'd done a bus tour before and were hoping for a bit of a breeze on the water in this hot weather. There are many boat rides of the "hop on and hop off "kind. They will take you along the two rivers, Spree and Havel, and even on the canal if you so choose.
It was an extensive trip of 3 and a half hours. We saw the most famous parts of Berlin, the government buildings, a few remnants of the wall, new fancy apartment buildings built in what used to be the former East; 1 million plus apartments without a kitchen because the logical thinking is that their clients work all day and go out for meals.
We learned that Berlin has more bridges (969) than Paris or even Venice (410). I just learned that Hamburg has even more :2485.
This is the famous and beautiful Oberbaumbruecke where in the 1800s citizens threw felled trees and logs into the water to make boats pay a tariff on their passage over the river. Only after paying did they remove the obstacles and let the boats through.
Other bridges were not architecturally important, but noteworthy in their surroundings. With this one you had to remain seated and duck down as it was so low.
Romantic or at least picturesque corners everywhere, especially on the canal.
Locks always make for interesting viewing. Here there was a man who was inside the restaurant watching the boat being heaved by more than 1 m to the higher level. He started to close the windows of the restuarant until his wife explained to him that it was not the water that was rising...
If you're into sailing, you're spoilt for choice because Berlin is surrounded by a myriad of lakes; also by many forests which can be explored by bike and on foot as well. More about that another time.