What a lovely thread, Zoe!
For me, it was visiting the Pompidou Centre in Paris in my mid-20s at the start of my backpacking trip in 1994 and finding myself in front of Matisse's Grand Interieur Rouge.
https://www.centrepompidou.fr/cpv/resource/c5egobb/rrg8AEM
I found the richness of the red absolutely mesmerizing and had real difficulty in tearing myself away. I bought the poster of the painting even though I still had six weeks of travel, and carried that triangle-shaped tube around with me all through Italy and Greece and on a bus up through Serbia back to Hungary. I had something of the same pleasure on Monday seeing the Matisses that form a large part of the Shchukin collection currently on display at the Louis Vuitton Foundation here. In this case, it was this huge room, FILLED with Matisses, which seemed almost to vibrate at each other with all the energy they were emitting.
Architecture-wise, there are so many. Someone above mentioned gasping when they saw a beloved work. My jaw literally dropped when I walked into the chapel of the Abbey at Melk. I had seen a lot of churches by then but the riot of rococo decoration there was simply over-the-top.
I love Art Nouveau architecture and had a special moment at the Horta House museum in Brussels, on a stairway where the light was coming in just so, and for a moment, you could almost imagine the museum as the house that it was, and filled with the people who lived in it. These pictures at the website don't begin to do the place justice -- they are VERY prosaic, nothing special about them!!! : (
http://www.hortamuseum.be/en/house/gallery
In Nancy, in eastern France, there's the terrific Ecole de la Musée de Nancy, an Art Nouveau gem - the house itself is wonderful, and it's also filled with all sorts of displays.
http://www.ecole-de-nancy.com/web/index.php?page=presentation-men
And finally, the opportunity I had to learn about the painters in Pont-Aven, Brittany, including Paul Gauguin, Paul Serusier, and Emile Bernard. Brown University has a long history with an art school there, and they run summer programs. I was lucky enough to be hired one summer to accompany a group that went to take advantage of the facilities for a writer's program. The group had its class sessions in what used to be the inn where Gauguin and others stayed; in fact you could see the room in one of his self-portraits. The best though was the tour that an art historian took us on through the "Bois d'Amour," the "Love Wood" where Paul Sérusier had his insight due to coaching from Gauguin (the painting, the Bois d'Amour/the Talisman, is in the Orsay, where there's a room devoted to these painters). This (American) art historian had an extraordinary ability to convey her love and passion and knowledge of this movement to a bunch of lay people -- I will never forget wondering how somebody with such depth of expertise could distil that expertise to be accessible to non-specialists in the field- as we stood in the landscape of the paintings we would go on to see back in Paris at the Orsay (she had reproductions with her as she addressed us of course). We also had the opportunity to visit the church in a nearby town where Gauguin painted The Yellow Christ. Of course now any time I get the opportunity to see anything about the Pont-Aven school, I'm there!!
http://www.musee-orsay.fr/en/collections/works-in-focus/search/commentaire_id/le-talisman-7071.html?no_cache=1&cHash=86d0a41f2f
http://www.comite-serusier.com/catalogue/191-interieur-a-la-lampe.html
http://www.musee-orsay.fr/en/collections/works-in-focus/painting/commentaire_id/paysannes-bretonnes-260.html?tx_commentaire_pi1%5BpidLi%5D=509&tx_commentaire_pi1%5Bfrom%5D=841&cHash=1b59d4e8f6