Berlin is phenomenal. I've been here for nearly 4 months now (I've been here studying Uni). Each of its neighborhoods have a distinct feel for it. If you feel like being an American with lots of money to spend? Go to Charlottenburg. If you want a great nightlife, go to Kreuzberg/Friedrichshain. History and memorials? Mitte. The list goes on.
The public transportation is cheap and extremely easy. The best system for a major city I've ever seen. The people are stone-faced, but mind you, they've just gone through the coldest winter in over 100 years

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Here is my recommendation list (touristy stuff and
local stuff).
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Museuminsel - Go to the Pergamon Museum and Altenationalgallerie. Avoid the Bodes Museum. The rest are worth it but go to the first two.
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Mustafa's - Really good Doner. It is literally outside the entrance for U-bahn Mehringdamm.
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Burgermeister - Best cheeseburgers in town. Literally underneath the traintracks for U-bahn Schlesisches Tor. Maybe a 15-20 minute wait, but they are worth it.
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Topography of Terror - Probably my favorite the most well done out of all the Nazi museums/memorials. It's free and you get to see part of the wall as well. Close to Checkpoint Charlie as well.
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Turkish Market - On Tuesdays and Thursdays, there is a Turkish Market between U-bahn's Kottbusser Tor and Schonleinstrasse. It's pretty good. And cool too.
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Victory Column - Don't be teased by the view from the Panorama Point in Potsdamer Platz. This is a statue in the middle of Tiergarten which gives a great view of Berlin. It has history and you can get a good taste of Tiergarten walking to it.
That's just a few of the things I can think of off the top of my head. Honestly, just walking around in non-touristy places is the best. Non-touristy = Potsdamer Platz, Brandenburger Tor, Friedrichstrasse, basically anywhere in Mitte or Alexanderplatz.
-You can google these, I won't detail them, but here are some really good/cool bars for you to check out:
Mein Haus am See, Dr. Pong, Clash, Oscar Wilde's and Weinerei..
Cafe's are endless. For the best, I suggest Neukolln/Kreuzberg around Kottbusser Tor. That's one of my favorite activities in Berlin to do, find new cafe's to visit.
Honestly, just avoid Alexanderplatz. It's overhyped and tons of people go there.
For nightlife, I suggest getting out at Warschauer Strasse and just find something you like.
Horrible city. Way too big and spread out, ugly, grey and dirty and pretentious as hell. Being German I've seen my share of shitty cities but Berlin takes the cake.
It gives the city flair. Honestly, it isn't even that bad. Neukolln/Kreuzberg/Friedrichshain etc etc are all unique in their own ways.
lol at the berlin haters
edit: also eat a schawarma instead of a döner at least once
I eat at a place near Rathaus Steglitz at least twice a week. Delicious. Schawarma > Doner
No real recommendations but you are lucky, berlin is the shit. Best city in europe.
My man.