The area you stay in is a great neighbourhood.
Winterfeldtplatz (the square you come across when going from U2 station Nollendorfplatz to Winterfeldststr.) has a farmers' market on Wednesdays and Saturdays, which I can recommend. The Nollendorfplatz area also has very nice cafés.
The other side, around U2 station Bülowstraße, was a largely Turkish neighbourhood when I lived there (in Winterfeldtstr. actually) a few years ago, with produce shops and Turkish eateries. It seems to have changed somewhat though.
Potsdamer Straße, the big street that takes you towards U2 station Bülowstraße, has plenty of buses that take you to various places in the city. And, of course, the subway line U2 - which runs overground - which takes you to many of the major sights.
You can get a day ticket or weekly ticket for the public transport, which will allow you to use buses, subways and suburban trains within the designated area. Your AirBnB host will probably have all the info for you, but the BVG (local public transport) information counter at TXL will also help you with this.