Vatican Museum
The Vatican Museum is truly amazing. There are things in there that I never knew were there, but I had seen many times before in textbooks. It was one of those experiences where I just couldn't believe I was actually seeing some things in person.
For example, the Laocoon Group, which I had come across before studying Latin.
And the School of Athens, by Rafael. This will be in any art history textbook. (I do recommend the audio guide which tells you who all the people are in the painting, like where Rafael painted himself in).
The amazing thing is that this painting in the textbook looks like its A painting. But actually it's one of many frescoes decorating a room, which is in a series of rooms painted by Rafael. Here's a view of the ceiling, so you get an idea of what the total environment is like.
And of course there's the Sistine Chapel, which is as magnificent as people say it is. You're not supposed to take pictures... And actually it's good that you're not busy trying to take pictures of every wall and every corner of the ceiling. You have time to enjoy the art! I think I listened to each description on the audio guide twice, just so I could better understand the biblical background. In all, we spent about six hours in the Vatican Museum.
Finally, a practical tip. Buy your ticket in advance on the Vatican Museums website. It carries a hefty €4 per ticket charge on top of the €15 entrance fee, but it is so worth it not to wait in line for two hours in 100 degree weather in the sun. The lines have a reputation for being long, and I can confirm this.