On first sight, Tegel seems to be a district far away from the adventurous downtown areas, but really the subway lane U6 takes you the the famous "Freidrichstrasse" in less than 20 minutes. The complex network of public transportation allows you to reach any point of interest quick and easy. No matter if you want to go all-tourist and visit the Checkpont Charlie, the Television Tower or the Brandenburg Gate or go all-punk rock in Kreuzberg and Friedrichshain.
Since you will find plenty of information about those things in many trip advisors and travel blogs, I'd like to point out some things to do in Tegel and close to it.
The outdated and snarky shopping mall "Der Clou" is housing one of the most exciting roof top bars of the city. The Clou Corner is a bar located on the top level of the parking lot of the shopping mall. The view: the runway of the Tegel Airport. A couple hundred meters away you watch the air traffic lift off and seconds later planes are flying over your head so close, that you can figuratively touch them. All with a drink of your choice.
This mall built in an old shutdown factory can provide you with basic and organic food. Its food court serves anything suitable for a quick lunch break. Of course, as in any other mall you can go clothes shopping, shoe shopping or get a hair cut.
It is located right next to the studio.