The new museums in this newest wing of the palace are not very popular. There's the Ephesus Museum, the Armory, and the Musical Instruments wing. You can walk briskly through all 3 wings (just over an hour) and skip the audioguide. There are a couple of nice pieces (esp in Ephesus), but the real attraction is the gorgeous architecture and breath-taking spaces, which you can photograph with flash in relative solitude.
Neue Burg was included in the combination ticket that packaged the Kunsthistoriches Museum and Treasury as well. I don't think I would have bought this ticket on its own, but it's a great option on a rainy day. The interiors are stunning, even without furniture.
A few notes, though: lockers are not free, and there is no coat check (you can leave your coat unattended, if you dare). There is also no W/C. Use the free coat check and W/C at the Treasury instead; it's nearby - keep your stuff at the Treasury while you are in the area.
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