I went with two friends several years ago in late September and stayed almost a whole week. The best visits were during the week when we almost had the whole place to ourselves. We were able to have conversations with several of the volunteers and really had a great time. They had signs all over the place, telling visitors to not touch the planes; every now and then, we'd see an older guy with a glassy eyes lovingly fondling a plane. I did it myself and never saw anyone getting grief for doing it.

I highly recommend the visit. Catch the films also.