you’ll be way out west at Messe then, but the public transport in Berlin is really excellent. Quick and cheap.
On the west side Charlottenburg has lots of good art galleries, and the Tiergarten is pleasant too if it’s not dark by the time you finish work. Then there’s Mitte (the city centre) but if you head up from Brandenburg Gate and the Holocaust memorial (both worth a look) you arrive in tourist central but there are some good museums and more galleries.
The cool kids hang out in Kreuzburg, Neukoln, or Friedrichshain, on the former east/west border down in the corner – all buzzy, artsy, good bars, restaurants etc. Bit like East London or whatever.
The extra cool kids now hang out in Wedding, in much the same way that all the London hipsters are deserting Dalston for New Cross/Peckham