Good areas to live and recommended Berlin city districts are as follows.
Prenzlauer Berg is popular with nice bars and restaurants nearby and the odd club, but it seems quite expensive. Seem to be a lot of apartments available in Charlottenburg that are cheaper but it has been described as not very exciting.
Generally, there are 'tourist' clubs, bars, and lounges near Hackesher Markt, which is in Mitte. But Mitte is large, so make sure you get a flat near Hackesher Markt or near a convenient U-bahn line. The locals also go out here as well, so you get a mix of people. There are places for yuppie locals. A lot of hip hop / house clubs, which attracts a young crowd (18-24). I found it to be a pain to go out all the way to Prenzlauer Berg or Friedrichshain on a consistent basis. Berlin is so big, you get lazy and don't really want to spend 30 minutes in trains to get from one 'neighborhood' to another.
Prenzlauer Berg is more studenty as well as some young creative types and couples. Nightlife here centers around the cultural center which houses a few clubs and a movie theater. Lots of cafes and some restaurants nearby as well. It's more lively and has more pedestrian traffic than Mitte.
Friedrichshain, is basically leftists, students, and various other people attracted to the cheap rents. Big flats here, for very little price. They have basically one street filled with bars and restaurants, but that's about it. If you want to go to a club, there are two right at the S-bahn station. But I found those to be not so great, because it fills with young high school kids.
Charlottenburg is boring. Older people who don't go out except to restaurants. But you also get younger singles who just don't like the eastern side of Berlin for one reason or another. And they do have a few clubs and lounges/bars too. Almost purely filled with well-off "Wessis" who you will find to be very different from the East Germans.
There are other areas too, depending upon if you are gay, artistic, whatever. Not that you have to live in such areas, but it helps to be near the places you go out in. Berlin is just way too big.
Both Prenzlauer Berg and Mitte are very large neighborhoods, so you want to be sure you live near the U2 line (I think the band's name was inspired by this U-bahn line). And I think there is Brit Pop / Indie night at SophienClub every Tuesday night. That's located in Mitte, right near Hackesher Markt.
There's Kreuzberg, which is mostly Turkish with 'pockets' of Germans (pretty interesting to witness actually). And then there's Schöneberg, which is nice but a central gay area.
Prenzlauer Berg and Mitte are what you would call posh (or chicy-micky if you're German). Expensive and full of tourists and yuppies drinking expensive cocktails in sushi bars. Pberg has a few redeaming qualities, but I generally stay well clear.
Friedrichshain and Kreuzberg are more gritty, although Fhain is being taken over by people spreading out of Pberg, and will be the same in a couple years. It's the 'hot' neighbourhood now, and a far cry from the leftist outpost it was a few years ago. I personally find Kberg much nicer. It's the only truly multi-kulti part of the city (not only white people, but also not a turkish ghetto).
Charlottenberg is a more established neighbourhood. It's quieter and not too exciting, but has nice, clean streets (which is something you end up longing for if you live in any of the above mentioned areas).
Treptow is very nice. Very quite area, five minutes from a large park on the river, 10 minute walk to Kberg, and a much lower rent than any of the areas mentioned above. If I want to go out, it doesn't take long, and when I come home at night I don't have to climb over drunks to get in the door and can actaully sleep without having 200 people outside my house (and it costs half of what I was paying in Pberg three years ago for a flat half the size).
Berlin is a massive city and you don't want to have to commute clear across it.
Schöneberg is very nice, but only if you don't have any problems with 'alternative lifestyles'.
Here is the website of a favourite part of Kberg. The population is about half Turkish/half German, there are several good bars and cafes, but not too much, and the nicest beergarten in the city. A couple of higher end clubs, too, but I hate techno and therefore stay away:
Pberg is the poshist bit of Berlin. Your neighbours will include the Bundestag President (Wolfgang Thierse) and most of the GZSZ cast (yuck!). Clearly this is in the more central parts (Köllwitz Platz, Helmholtzplatz). There is more affordable accomidation, but as you say, 15 minutes from the U2 (which most would no longer consider Pberg), and in a small flats in unrenovated buildings with coal heating.
I currently pay €380 warm in a renovated historic building with hardwood floors and a balcony. That'd cost you about twice as much in Pberg. Having said that, my favourite cafe for breakfast and the best weekend market are both in Pberg.
It just gets a bit annoying when every cafe is full of people typing away on laptops who proudly tell you they are working on their 'manuscript'. In the rest of the world these people would simply be called 'second year students'. Pretentious, I guess, would be the best word to describe the area.
The Saturday Berliner Zeitung has the most comprehensive listings in the city.
If your looking further out why not try Köpenick!
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