What is the name of the famous tourist town in Italy slammed up against the Meditterean Sea and the buildings are built like a collage, one on top of the other, all the way up a large hill? Hopefully, someone will know what I am talking about!
One of the Cinque Terre - Wikipedia ?
I’ll check both out. Perhaps both are equally gorgeous! 
Wish I could go see it for myself!
Manarola is the one, but Wiki does say similar villages popped-up over time. Breathtaking!
There are steep hills and hill-climbing villages across the way from Capri IIRC (Amalfi Coast?), but generally the postcard-perfect villages are those Cinque Terra
There are villages like that on some of the Greek islands . . . but with subtler colors.
Positano.
I, too, was thinking Positano, on the Amalfi coast near Naples.
Thira, on Santorini, springs to mind. It’s stunning.
It seems that necessity has brought forth similar architecture in more than one place. A bit of advice, though: If you plan to through Cinque Terre by train and enjoy the scenery: Don’t! The train goes in a tunnel literally through the whole area and you won’t see a thing unless you get off at each and every station or take a walk between the villages.
There are some towns like that in the US. Obvious examples that I can personally attest to are Brunswick, MD and Harper’s Ferry, WV. The pictures do not do them justice - they really are very steep riverbank towns. There is a spot in Harper’s Ferry where you have to climb up a rather long set of stairs to literally cross the street. Harper’s Ferry is also a very storied town in terms of US history.
You’re thinking of the Amalfi coast, which consists of Salerno, Amafli, Positano, and Sorrento, in that order. There are, of course, many tiny towns along the way, but they’re not as famous, I don’t think.
Positano was featured in Under the Tuscan Sun, if you recall.
