We went to a one-room exhibition in the Ashmolean museum: Dimensions - the mathematics of symmetry and space. It felt a bit thin but I liked the assertion that time could be the third dimension rather than the fourth, in films, for example.
The virtual reality section at the end had a very neat demonstration of how there are dimensions between whole numbers - a new concept to me. I sat outside a cube (three-dimensional, obviously) then moved inside it as bits were removed and it became a Menger sponge, with 2.727 dimensions. (It was one of those things I understood clearly as it was being explained but couldn't put into words afterwards. I might have to go back.)
The VR suffered an amusing programming glitch mid way through, with the result that what I was watching suddenly leapt to my right so when I put out my hands, as instructed, to spin a 4-dimensional object they hit a very real and not-at-all-virtual wall.