We have been looking on line and in Ricks guide book. We plan to take public transportation and no alcohol. Some history but also shopping 18 yr old girl.. We really want to stay central to most of what we are doing. Thanks
Berlin is a loosely structured city with multiple "centres" and major sights spread out between them. If your big priority is access to public transport, I would suggest either the area fairly close to Alexanderplatz or the former centre of West Berlin in the area of Zoo Station and the Kurfuerstendamm. The current centre for upmarket shopping has now moved away from the Ku'damm to the area south of Friedrichstrasse railway station and around Gendarmenmarkt, though.
Adding to what Phillip wrote... unlike many cities in Germany, don't assume the Hauptbahnhof has a good central location... although there's several hotels in the immediate vicinity, it sits sort of in an isolated no-man's land of construction. Berlin really doesn't have a "central location".
I stayed in the ultra-modern Maritim Hotel near the Friedrichstraße rail station. There's quite a bit of very high-end shopping in the immediate vicinity, and you're within easy walking distance of Brandenburger Tor, Unter den Linden, Museum Island and the Reichstag. The location near the Friedrichstraße station also means that you can easily catch public transportation to anywhere else in the city. But it isn't exactly cheap.
I also stayed at the Steinburger Hotel right by the Hauptbahnhof, which was as nice as you'd expect for this up-market chain. But as noted, not a great location.
Not too long ago we spent several nights at the Hotel Askanischerhof. Our room was gigantic, included a sitting area like a sunroom facing the street, and furnished in what I suppose would be called "old world charm"...fun. Breakfast was included, there is an elevator. Reasonably priced by our standards. It is located on K'dam and surrounded by very high end luxury stores and tons of shopping. Convenient to transportation near Savignyplatz and the many decent, moderately priced restaurants in that area. The KaDeWe department store was maybe a 20 minute walk away. We don't speak German or Dutch, but got a chuckle from the two Dutch couples we chatted with as we walked to this store. According to them, the name comes close to the Dutch for "take your money"' or something like that. Sights are spread out in Berlin; being near a transportation hub was important to us. Good luck.