I thought the Pergamon was worthwhile in 2015 even with the altar not accessible. The Ishtar Gate is something else.
Berlin has a lot of good art museums. Whether any of them will make up for the closure of the Neue Nationalgalerie depends on what periods of art you enjoy. Be sure you know what all your options are.
I enjoyed the Museum Berggruen in Charlottenburg and the Gemaldegalerie at the Kulturforum.
I see that InYourPocket has a Berlin guide online. The IYP guides are usually updated every 3 or 4 months, and the ones I've looked at for Poland and Ukraine have been good about mentioning current temporary exhibitions, which is particularly useful information when you're planning visits to art galleries. They've also generally been accurate about hours of operation.