Bike hire, it’s cheap and the city is mostly pretty flat and great for cycling. We used fat tyre bikes (loads of places round the city)
Old east berlin is where anything a bit more alternative is located, the most interesting art places etc.
Clarchen’s Ballhaus is an interesting place to go, crazy building, nice pizzas too http://www.ballhaus.de/
Get free listings magazines in bars for art / clubs etc, changes so often no one will be able to recommend anything of that kind reliably. Tripadvisor might be good for restaurants, so many visitors to the city it’ll get tons of reviews for anywhere, although to be honest i usually just wander around and look at places, it’s quite a good city for that.
Tons of historical stuff, depends how much depressing holocaust stuff you can take – the holocaust memorial is very moving in an extremely bleak way.