Whenever I fly into Berlin I spend most of the time in Potsdam, with day trips to Berlin. Some of the sights mentioned above are in Potsdam, so I would recommend at least a day trip there. About 35 kms away. They have recently rebuilt the Stadt Schloss and the alter Markt. Many of the Garde barracks can be seen as well, etc.
Obviously, some of the sights in Berlin mentioned above are worthy (and a priority) of being seen on a first time trip there. It takes time to see all the sights and museums. A quick trip to Postdam will give you a less touristy atmosphere, and will give you an idea of which you might prefer. In case you plan a return trip.
Zitadelle Spandau has a nice museum, but as it is about 15 kms west of the center of Berlin, might be tough to add to your itinerary. It had some nice Imperial, and earlier, headgear and firearms. Was only there once, but I added it to our recent trip as a good place to spend the last night before flying back.