cheep double rooms in Berlin!

City centre is a question of definition in Berlin. What is the centre for Berliners might not be the centre for tourists. And Berlin is a mixed box of many centres.
"Nice and cheap", well, cheap isn't always nice and nice not always cheap.

City East: check www.eastsidecityhotel.de in Friedrichshain - Friedrichshain is a bit out of the historical centre and a bit rough (noisy) for my liking.
or www.maerkischer-hof-berlin.de in Mitte - it's in the old Jewish quarter, gentrified and posh by now in places, but in the middle of scenic nightlife.

City West: check Hotel Transit in Kreuzberg (don't have url at hand, but google will help). Kreuzberg is full of nightlife, oriental centre of Berlin (i.e. Turkish community around) and very lively and interesting.
or www.charlottenburger-hof.de in Charlottenburg

The only hotel I ever stayed in (t'was a freebie, I usuallly stay with friends) was Charlottenburger Hof. It's in one of my favourite areas, the centre of the old West with loads of nightlife and shopping around.
What I liked was the computer in every room with free internet-access.

Even cheaper are hostels, where you'll get private rooms, too.

It really depends what you mean by cheap. I like Hotel am Anhalter Bahnhof, which is close to Potsdamer Platz and there is a direct bus connection from the main station (M 41). Prices are very resonable for the location: http://english.hotel-anhalter-bahnhof.de/

for old style DDR atmosgfere: www.ostel.eu, very near the East station, in/near the old DDR prunkallee

Depends on what you mean by cheap. Hotel Jurine is a very nice small hotel on the border between Mitte and Prenzlauer Berg. All the cafés, restaurants, shopping and night life of Kollwitzplatz, Kastanienallee, Zionskirchplatz, Rosenthaler Platz, are within walking distance. Hackesche Markt is a short tram ride away. Two tramlines, an U-Bahn (subway) line and nearby S-Bahn (city railway) make all parts of Berlin easily accessible. In a funky district with lots of atmosphere. Kastanienhof is also very cozy, but right on the busier Kastanienallee in the same district (my neighbourhood). These places are not hostels, though, and don't charge hostel prices.

In June, I had the "Deal of the Century" from Priceline.com...

we stayed at the Mariott Courtyard Berlin City Centre for 4 nights at $46/night !!!

an odd location... but central... and 1/2 block from the Metro.

I don't know if it was our timing?... but it might be worth a try.

I think rack rates are about 120 Euro/night.
there are other berlin & area Mariotts starting at about 45 Euro/night...
but some are not in the Centre.

good luck!