Ask why it appeals to them. Tell them what you like afterwards, and why it appeals to you. Pick out your favorites too, and see how much you agree on. For older kids, a '10 Worst things in the museum' list may be of interest. It is an interesting exercise to discover that your child may have 'opinions', or 'personal tastes'.
Many art museums offer tours.
Some offer art classes. In larger museums, take some time to annoy the security guards. Ask them some questions. Odds are they are quite well versed in the things they watch over and are happy to have someone show an interest. There are lots of things that can spark discussion.