I thought it was such a useful discussion-starter that I'm reproducing it here, for any of my readers to answer in the comments:
1. The person answering these questions
a) is on the autism spectrum
b) is a family member or close friend of someone on the autism spectrum
2. What cultural insitutions do you visit?
3. What is helpful before or during your visit?
b) website information
c) audio tour
d) information in print
4. What is unhelpful during your visit?
5. What would you change about cultural institutions that would make them more inviting to attend?
6. Name some cultural institutions that you think offer a pleasant experience.
For me, the biggest issue with museums, galleries and the like is crowding. If a room is too crowded, I can't pay as much attention to the exhibit because I also have to pay attention to all the sound and movement around me, and, when I'm paranoid (which is not all the time; the need to attend to all sensory stimuli equally is constant), I also have to devote mental space to positioning myself strategically so I am farthest from any knots of people. This can be a pretty demanding activity if those knots of people are constantly moving, as they usually are in a museum or gallery.
That happened when I visited the Smithsonian Institution's National Museum of Natural History in Washington; the noise and crowds had been pretty overwhelming the whole time I was there (I made it through one exhibit and part of a second one), but when I left the huge room the first exhibit had been in for the narrow hall the second one was in, the press of people got a lot worse, and I noticed I was losing the ability to speak or think. My entire consciousness was being absorbed by noise and movement, and everything took on a really scary appearance. I stopped looking at the displays, not having the available brain space to understand them, and started keeping to corners and walls, taking temporary refuge until I was able to muster the strength to find my companion and tell him I needed to leave.
What that incident tells me is that the severity of my reaction has as much to do with the available space as it does with the absolute number of people present. I could handle the same number of people in the mammal exhibit, since that was a huge room in which they could all spread out (and in which the open spaces helped me not to feel trapped). I also tend to do fine at outdoor events, like zoos or Renaissance Faires. Movement is also a big deal; I have no trouble going to the theater, even though there are often huge crowds, because they tend to stay put and are quiet most of the time. (I stay put at intermission, though, to avoid that crush). I also go to the Heart of America Shakespeare Festival whenever I can; really, my main barrier to theatergoing is convincing my family members to take me out to plays.
One indoor event that handled the problem of crowding well was an exhibit of preserved human bodies (I can't remember if it was Body Worlds or Bodies Revealed) in Washington DC. What they did was just to pulse the flow of people through the exhibit; one or two parties started the tour at a time, so that the other people would always be a few rooms away. It worked really well, as far as my ability to enjoy the exhibit without the crowds getting to me, and it wouldn't cost anything to implement, as a staff person already has to be there to take tickets. He or she could just perform the additional duty of regulating traffic.
Those are my experiences; what about y'all?