Dear Andreas !
This one:
http://www.bogota.de/default.aspx
I can recommend , it has charme, style, history (see webpage), friendly staff, famous visitors, is central Berlin and is AFFORDABLE.
Only for your MAIN CONCERN = internet access: that I don't know about, but you could ask them via email.
... and here some private travel suggestions (some of historical value) in case there is spare time ...
10963 Berlin: Anhalter Bahnhof ruin und süd-südwestlich davon hinter dem Tempodrom noch erhaltener Bahnsteig des Gleisfächers
10117 Berlin: Café Einstein, Unter den Linden 42
10435 Berlin: Konnopkes Imbiß, Schönhauser Allee 44 A (famous ?but good? Currywurst)
10437 Berlin: restaurant Onkel Ho, Gleim Str. 10A (vietnamesische Küche)
10623 Berlin/Charlottenburg: Patisserie Stephanie Albrecht Fasanenstraße 29
10969 Berlin: italian Ristorante sale e tabacchi, Rudi-Dutschke-Straße 25
10969 Berlin: Jüdisches Museum, Lindenstrasse 9-14
10999 Berlin-Kreuzberg: Würgeengel, Dresdener Str. 122 (famous bar)
12047 Berlin: Jimmy Woo, Friedelstraße 24 (Indochina Restaurant, Tip: Kao Num Chien= Northern Laotian soup with a special order of pho noodles)
13507 Berlin: Florida Eiscafé in Tegel Alt-Tegel 28 täglich 11-20 Uhr
bye, best wishes for your stay,
FrankieS