This museum is fabulous. If you have any interest in history, you will be bowled over. Don't expect to do this museum quickly. The headsets, which come with your admission ticket, are a must; the commentary is very fine and illuminating. The two big things to see are the Pergamon Altar and the Ishtar Gate. Pergamon was a Greek kingdom in Anatolia, and this altar, now mounted into a temple setting, was excavated and brought to Berlin in the 19th century. You will learn a lot about ancient Greek life if you view this incredible monument in detail. Hardly less overwhelming is the Ishtar Gate, which will take you as close to being in ancient Babylon as you will ever get.
There is a pretty good pizza place, and other cafes and little restaurants, which you will pass as you walk to the museum from the Friedrichstrasse subway station (the closest one to the museum). One of these is a lunch possibility. Also on the Museum Island is the Berlin Cathedral, where the Hohenzollern family, the former rulers of Prussia and Germany, have their tombs. It is interesting.