I'll start with some practical stuff: when you go to Berlin for a few days it's good to get "Berlin Welcome Card" which is a ticket for all kinds of city transport and at the same time allows you to get a lot of discounts in restaurants or tourists attractions. You can get it in tourist's information points and all points of sale are shown here.
U-bahn and S-bahn are the best kind of transportation - they are quick, frequent (in a few-minutes intervals) and they don't get stuck in a traffic. The traffic net looks like a spider's web with a ring around the centre. If you don't travel far, bus is also fine. There is no possibility to get lost in Berlin - it's very well marked and if people see you with nose in a map, they just come to you and ask where do you want to go.
There is also nice thing called "Free Tour". You can sign for this in the Internet. It lasts approximately three hours and isn't quite free - just instead paying in advance you pay tip as big or as small as you want at the end of the tour.
I definitely recommend couchsurfing for accomodation, because you can meet many very interesting people and go to places that you normally wouldn't know about. I also recommend Main Station Hostel which is quite far north-west, but it's clean, with big spaces and nice staff.
Berlin wasn't my love at first sight - it seemed very ugly, dirty and grey and smells terribly, but after a few days I was really impressed by architecture, peoples hospitality and remains of history.
At the first evening when we were looking for our couchsurfing host's flat we were a bit surprised by building labeling because we were sure that we're on the right street only thanks to map, also the number we thought as a number of a building was a number of the entrance doors. Flats were labeled by number of the floor and sequence number (if flats were on 1st floor they were marked as 1.1, 1.2, 1.3, on the second 2.1, 2.2, 2.3). In our host's flat we met two Polish people who were also his couchsuurfing guests.
We went on the Free Tour to see Holocaust Mahnmal which for me is absolutely stunning (a memorial for murdered Jews made from almost 3000 stone blocks), Brandenburger Gate, twin French and German Cathedrals which are different only in height, Ministry of Finance with socrealistic paintings on the wall, Checkpoint Charlie with images of soviet and american soldier and we were on a car park where used to be Hitler's bunker.
After the tour we went to the rotating restaurant in Fernsehsturm (TV Tower). Restaurant makes 360 degrees round in one hour. We were watching Berlin's panorama and we could see the big difference between eastern and western part of the city.
At the evening Tim, our host, invited us for the jam session which took place in the basement of old Stasi building.
Next morning we went to the hostel to leave our things and then we spent almost an hour in trains to get to Reichstag where we had booked entrance to the dome.
When we got to the dome it turned out that we have booked entrance - but for the next day. When we were in the train a building with a manekineko (Japanese figure of a cat bringing luck) drew my attention, so I decided to give it a closer look, but before that we went to Kreuzberg to eat kebab from Mustafa- the most delicious I ever ate, perfectly flavored and full of fresh vegetables.
We also went to see Schokowelt (Chocolate World) which appeared to be just regular shop with Ritter chocolates and Currywurst Museum which is the craziest idea of sort - we saw a currywurst trucks, listened to people's quotes about sausages or learnt some trivias and recipies. We also tried a cup of currywurst (no, there's no mistake. It was a cup of currywurst).
First night in Berlin wasn't totally calm because in a middle of a night we were waked by lady screaming "NEIN!, NEIN!". Luckily, that was only a bad dream.
Next day we saw the dome, Salvador's Dali exhibition (rich and full of works from different periods and techniques). We were advised to go at Warschauer Straße by Tim's friends so we went there. At the train station entrance was a girl singing and playing guitar, surrounded by quite a big crowd, there were groups of tourists and young people drinking beer on the streets, there was a huge speaker in the doors of one of the shops and we could hear loud music from it, and on the bike path we saw a guy with a beard dressed in white lace dress riding a bicycle.
Last day we spent in Potzdam - great change after Berlin - small, with rich scent of flowers and really beautiful. We were in Sanssouci Gardens where we saw Neue Kamern Palace, Church of Peace, New Orangerie and works of great painteirs in Picture Gallery. The complex is very impressive, rich interiors are thrilling and precise architecture of garden are really nice. I think that next time we'll need for Potzdam at least two days.
Despite first bad impression, Berlin turned out to be amazing city. I think that words of a Peter Fox song "Schwarz zu Blau" describe it the best:
du kannst so hässlich sein,
so dreckig und grau
du kannst so schön schrecklich sein"
You can be so ugly,
so dirty and gray
You can be so wonderfully terrible