Originally Posted by FrancisA

Gate 4 which most BA flights use has both a cafe/bar and a fairly substantial duty free shop.

On the travel to and from TXL I'd say a taxi was poor value when you can get 24 hours unlimited travel in zones/ringen A-B (i.e. all of central Berlin includingTXL) for 7 Euros.

That ticket would cover the trip to TXL, an excursion back to say Alexanderplatz, Friedrichstrasse or Ku'damm, return to the OP's hotel and then back to TXL. All easily doable in the time available to the OP. I'd add a zero after 7 for the price of doing that by taxi.