One thing that everyone will want to do in Berlin is to make an excursion to Potsdam. Indeed, if your plans include renting a car or driving to another city, you might want to consider renting the car and then staying in Potsdam for two nights, which arrangement would afford you both transportation and the leisure to see the town and its attractions without rushing.
One can easily travel to Potsdam on the S-Bahn; it takes about 25 minutes. From the terminal at which you arrive there are buses that will take you to the palace of San Souci or the Neues Palais. You will want to get an early start on this excursion, because there is a great deal to see, too much for one day; choices must be made, probably. San Souci, Friedrich the Great's pleasure palace, is memorable, and the grounds are magnificent. You will want to walk all over, and be sure to see the Chinese Tea House, with its exquisite decoration.
In one of the rooms of the palace you can see the chair in which Friedrich the Great died; and for some unaccountable reason, the guide who took my group (English speaking) through the various rooms failed to mention this item, perhaps on the theory that Americans aren't interested in history?
Nowhere near the palaces, which are situated above the town, is the Cecilienhof, once a royal hunting lodge, today a hotel, the place where the Potsdam Agreement was signed. There is a museum room with the table, etc. You could have lunch, tea, or dinner here, or stay the night. There are several things to see in the town, but the hotel is not convenient to the most major sights. (This is where a car would come in handy.)
Probably you will not get back to Berlin by train before 5:30 or 6pm at the earliest; so you may not want to plan a taxing evening for yourself.