Alas, I last visited Berlin in 1991 (du heiljer Schreck!), so most of my practical information is likely to be out of date. As a result of its history there are very few old building: in fact, it's hard to find anything dating from before 1820 ...
That said, Schloss Charlottenburg (which is older) is worth a visit, so too is the tiny historic centre, part of which has been reconstructed - and looks rather obviously artificial. Stroll down Unter den Linden, explore Prenzlauer Berg and also Kreuzberg including the Viktoria-Park.
Berlin is famous for its museums, especially the Pergamon-Museum and the Museumsinsel more generally.
It's a very lively, vibrant city. Unless things have changed out of all recognition since my last visit Oranienburger Strasse is worth a visit late in the evening.
Incidentally, in the older parts of the city, the buildings aren't numbered in the standard way: instead they are numbered the full length of one side of the street, e.g. 1-200 north to south, then say 201-400 south to north on the other side of the street. So in the case of Friedrichstrasse, which is about 2.5 km long it can be a nuisance. Better street plans give details of the house numbers.
Of course, much of the centre has lots and lots of new buildings, and I've heard it's still a vast building-site and not particularly cheap ...
Btw, I hope the more nationalistic locals have finally dropped the habit of calling the city the
Reichshaupstadt .

The only German-speaking city that qualifies for that label is Vienna.