Where is the best area to stay for the weekend in berlin?

Gosh, there is so much and one weekend isn't nearly enough.

Without a shadow of a doubt I recommend you stay at the Hotel Tiergarten. It is located near a small park called the Kleine Tiergarten and is about 150metres from the Turmstrasse UBHf and about 15 minutes walk from Bellevue SBHf. The bus TXL from Tegel airport stops almost outside the front door.
This place is excellent value, serves a breakfast to die for and has amazing ceilings (it's a converted rich man's house). If you can't get a room at the Hotel Tiergaten then try the Hotel Park Consul. It's very close but is a bit more expensive.

From here you can be at the Zoo (U & S Bhan to everywhere in the city) in 10 minutes (or walk it in 20 minutes through the park), Friederichstrasse in 10 minutes, Alexanderplatz in not much more and 15 minutes to the Memorial Church and Europa Center area. The big park called the Tiergarten is about 5 minutes walk.
Three more stops on the U Bahn and you're at the Potsdammer Platz. This is a tower-block watcher's delight. Every tall building is radically different from each other.

For a weekend you should visit:
the Pergamon Museum (Museum Insel about 10 mins from Friedrichstrasse Bahnhof);
the Potsdammer Platz (be hungry);
Treptower Park (huge Soviet War memorial), it has its own S Bahn station;
the Europa Center. Good but not cheap shopping. Try and figure out how the water clock works, it'll drive you mad;
All the shops up and down the Freiderichstrasse as far as the Checkpoint Charlie (about 2km);
visit the Nickolai Viertel and sample a beer at the Georg Brourie (sorry about the spelling);
the Reichstag is worth a visit. It's free but you may have to queue for an hour to get in and security is tight. Great views though;
if you like views you can go up the television tower and enjoy the gallery or eat in the revolving restaurant (costly);
Go to the big shop called KaDeVe, it has a superb chocolatier level near the top floor.

If you have time and the weather is good then take a river boat trip and/or a S Bahn ride to Spandau (nice suberb) or to Grunewald (big lake, boats, nude bathing etc).

You should buy a "Welcome Card" when you arrive. This is an all-modes (bus, tram, U & S Bahn and RE trains) travelcard which also gives you discounts for a huge number of attractions. See the BVG web site (link below) for details.

Hints -
they will like you when they discover that you're English (I'm not being jingoistic, it's just the way they are);
don't eat "curryworst", it's muck;
don't eat the "fish and chips" near the Europa Center, it's as if they'd read about them but never seen them;
the best introduction tour is the bus 100 from the Zoo as far as Alexanderplatz. It goes past most places of interest in the centre;
Berlin does not have a "Centre" it has lots of hubs. This is probably a consequence of partition;
don't buy bits of Wall - they're all fake now;
ignore street beggars, they're not really a poverty stricken country and the police have trouble with fakes if tourists keep feeding them, some can also be agressive;
the best way to find a Berliner policeman is to cross a road against a red man, they appear by magic;
stay away from the eastern suburbs unless you're with a friendly local;
Berlin has hundreds of small corner pubs and dozens of micro-breweries, drink local beer rather than the common stuff - it's much better;
trams do not give way to pedestrians;
the southern suburbs back streets around Neukoln are gas lit - very romantic and fairly safe but don't get lost.

Berlin where?
Germany, New Jersey, The Carolina's..

What Berlin?????

Try to find a place somewhere central, like in Kreuzberg or Mitte. There's a hotel called Angleterre that is very central and ok as far as prices go.

East Berlin all the places of interest are in that part of the city