The welcome card depends on what it offers and where you want to go. I have found these less good value in most cities, because a lot of the offers are things I'm just not interested in or won't have time to do.
Unlike London, travel costs and entry costs are very reasonable in Berlin, so once you have got in from Schoenefeld you may find day tickets for AB good enough. There are two public double-decker buses that travel the main city tourist routes - think, 99 and 101 but may be misremembering - and the general low cost and reliability of the buses and trains is wonderful.
It';s a big city with many diverse suburbs so where you eat and drink may be determined by what's local to where you are staying. We stayed near Adenauerplatz and there is a whole batch of inns and sandwich shops round about.
What I enjoyed doing was: Checkpoint Charlie Museum; walk from there to the Brandenburg Gate (think it's got works on there at present); the Pergamon Museum which has a reconstruction of a fantastic Greek temple and of part of the ancient entrance to Bablyon; less pleased with the national Museum adjacent, bit of a hike round rather boring displays; the Television Tower - nightmar queue but fantastic view when up there; quite near the TV tower is all that is left of 'old' Berlin, literally a few streets, but a quaint area in the general bustle of the city, with lovely restaurants etc; I wish I had been there before the wall came down, to see the effect and the diferences, but there is hardly any wall left now; the art collection and archaeology museum out to the northwest of Adenauerplatz was brill (for me - I know it's not everyone's idea...); walk through the Unter den Linden or hire a bike. In the time you have you could also go out to Sachsenhausen and make yourself thoroughly miserable at the concentration camp site.