Unfortunately the Klimt museum is not worth a visit at all. It was one of our top destinations, and a grand building but a total let down. Apparently the famous picture "The Kiss" which is sold on coffee mugs, calendars, kitchen magnets, etc was not there. And then some of other famous ones were removed a few years ago. (The model in some of the paintings ended up with them, and specified they be left to the Austrian government when she died, but she died, and then her husband left them to his kids. The family fled the Nazis, the paintings ended up in the museum, and then 60+ years later, the ladies' niece sued to get them back as Nazi looted art, and promptly sold them for $325M). Apparently the Austrians spent tens of millions on this great museum to honor their most famous painter, but now there are none of the well known paintings left. So save your 11 eu each
The Modern Museum looks great from the outside. Unfortunately there is no real art inside at all. Most of it was literally stuff they got from a storage locker in NYC in 1990's. It was the most boring "exhibition" i have seen in my life.
Perhaps this is why Rick does not highlight the museum quarter - there is really not much to see.