Some places to make standard work like copying files or sending a fax can be found in the following links:

http://www.copyplanet-berlin.de
http://www.centralstation-berlin.de/
http://www.kopierladen-berlin.de/

Here are some recommendations that I found surfing:

http://www.hotspot-locations.de/modules.php?name=HotSpots&op=hotspot_query&hsl_countryhs=DE&hs_state=&hs_city=berlin&hs_operator=&hsl_type=BarCafe&hs_access_box=on&search=Suchen

Individual places:

All Starbucks in Berlin: Hackescher Markt, Alexanderplatz, etc.

St.Oberholz (Rosenthaler Platz)
Aufsturz (Oranienburger Strasse)
Macondo and Szimpla (Boxhagener Platz)
Kaffee und Tee and Sanatorium 23 (Frankfurter Allee)
Manolo (Eberswalder strasse)



 

There is a place where you can drink and eat as much as you want!. and you pay 2€, of course if you really like it you should leave a little more as a tip. It depends on you :-)

http://www.weinerei.com/

I found a wonderful site to go and sky in the night!.. .you can try and do it... yes..skating in the night!!

http://berlin.skatebynight.de/strecken/index.php

A taxi can be taken from any place or can be called to come pick you up at anytime you want, even weeks.

Here are some phones that you use if you are in need of a taxi:
030 20 20 20 (Taxi Berlin)
030 44 33 22 (Taxi Funk Berlin)
030 26 3000 (Quality Taxi)
03021 02 02 (Cityfunk Berlin)

 If you only want to know about them, how they think, what they do you can visit a blog about them (only in German) http://www.taxiblogger.de/