To get a good feeling for the atmosphere in our city, just go for a walk in our neighbourhood: You will find countless cafes of every style with real good coffee for a reasonable price, little restaurants of at least ten different countries with lunch menus, nice boutiques, antique shops, delis, art galleries, book shops and more. You should visit one of the weekly markets that are to be found on various places within walking distance, its best being the one at Winterfeldplatz on Wednesdays or Saturdays. If you like dancing you could go to the Havanna, a disco just round the corner. You can keep fit in the Elixia Studio at Prager Platz, or join a yoga-lesson in the Akazienhof. The traditional Odeon cinema round the corner shows films in their original versions, or if you like independent films, have a look at the Xenon. If you prefer a walk in a more natural surrounding, stroll through the Rudolf-Wilde-Park, passing the famous Schöneberger Rathaus on your way. On Sundays it's worth while visiting the flea market there, where you might find some interesting artefacts. Should you be up to a good swim, there is the Stadtbad Schöneberg, a public swimming pool (indoor and outdoor) within a 3 minutes walk. A bit further away (a 20 minutes walk) is the newly installed Gleisdreieckpark that you can also explore by bike. Bus M104 takes you to the Tempelhofer Feld in 15 minutes, an absolute 'must-do' because it is unique: Having been Berlins central airport until a few years ago, the area with its 300 hectares has now been transformed into the largest area with an animpeded view in central Berlin, where you can jog along, cycle, rollerskate, walk, have a picnic, visit new urban gardening projects, and, and, and ...
I didn't mention the typical Berlin tourist attractions that you surely know. They too are not far away, but about them you can find everything in any travel guide.
Although Berlin is the most interesting German city, you might want to visit other cities as well : Hamburg (2 hours away by train), Leipzig (1 hour), Dresden (2 hours).