I’d definitely recommend an hour or 2 at Schneidersladen. It’s actually not that hard to find…get a U-Bahn to Kottbusser Tor, when you exit the station, look for a supermarket just over the road & it’s above in the same building, accessible by a buzzer on the right. The people there are super-friendly & you’ll be able to try out loads of great stuff.
Tempelhof is nice, as someone said earlier. The experience of cycling on a runway on a nice day is pretty awesome!
Avoid Treptower Park after it gets dark. We had some issues walking through there at night last time we were there (turns out it is a dealing hotspot).
Kreuzberg has some good bars, as does Neukolln. If you’re into veggie/vegan food, Voner does maybe the best vegan kebab I’ve ever had!
There’s a great flea market at Mauerpark every Sunday, you can watch karaoke at the amphitheatre in the Park in the afternoon, which is fun when the weather is good.
Avoid a record shop called Frank & Josef like the plague…the guy who runs it is one of the rudest people I have ever met. Googling it after the event reassured me that I wasn’t alone in this (if you fancy a laugh, it’s worth reading their reviews).
Finally, if you’re cool with heights, the TV tower at Alexanderplatz will give you a great panoramic view of the city.
Enjoy…I love Berlin.