Since you are travelling transatlantically I assume that you're departing from Tegel Airport. If so, the transportation will be by bus and you'll want to be fairly close to the airport to avoid traffic and so you don't have to get up too early, so I'd suggest staying somewhere fairly close to the Hauptbahnhof where the JetExpressBus to Tegel has its city centre stop closest to the airport. It's not the most characterful of areas but it's safe and you'll be able to get the S-Bahn elsewhere in the city for sightseeing.
Personal suggestion for the evening: since it will be light for a long time, get a day ticket and do the cheap unofficial sightseeing tour. Take the S-Bahn elevated train to Zoo station and from there get bus 200 (double decker) all the way to Alexanderplatz through the centre. Walk towards Hackescher Markt and eat somewhere around there, get the S-Bahn from Hackescher Markt back to Hauptbahnhof and go to bed. Get up early in the morning and get the JetExpressBus to Tegel.
If by any chance you're flying out of Schoenefeld in the morning you would be better staying somewhere around Alexanderplatz and getting the train from there to Schoenefeld in the morning. But I'd still suggest the S-Bahn/bus-200 loop as a way to see most of the central sights.