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. Historical paintings, or characters or events from stories thay you can explain to them, or perhaps they can explain to you. Scenes of passion or violence that, since they are expressive and frozen in time, you can talk about together and broach some of life's harder subjects.
Most museums have a little gift or reprint store.
Your child may find a post card or small poster of one of your favorites to take home. There are online portals to a number of museums. Check around on the web. If you have access to Usenet, there is an online newsgroup named alt.binaries.pictures.fine-art where some beautiful scans are posted regularly. But it is a neat thing to do together, as long as you do the steering.