Was at the museum and factory tour just three weeks ago, had quite a different experience. The museum is relatively small, but had some very interesting bikes: one of their earliest racers (looked almost like a bicycle with a very small displacement engine and a megaphone pipe) as well as one of the newest racers and many in-between such as Mike Hailwood's machine, as well both a beautifully restored original Scrambler and a new one, etc.). The museum staff was accommodating and didn't mind if we took pictures of ourselves with the bikes. We fortunately were just leaving as a school group arrived, I doubt the kids had any appreciation of the fact that they were to go to the Ducati museum as a field trip (I recall going to see a dairy when I was a kid).
The factory tour was good, though we had to book it several months in advance to get in when we wanted. There were engines being assembled, Scramblers and Monsters on the assembly line, and (my new dream job) a guy who gets to make a dyno run on every bike before it goes out the door. Kind of pricey, I think it was 140 Euro factory+museum for the four of us, but afterward we decided it was worth it. I think the bulk of the money goes to some kind of Ducati-supported charity, if that makes a difference.
Relative to LadyBishop above, maybe they got their act together since she was there?