Adding to my previous post, I'll note some specific recommendations. I made a list on this map (which is a picture of a physical map. Location on Google Maps is
here.)
I'm sure others will have many other recommendations for other sites on this map. Here are mine, as labeled on the map:
1- Zichron Moshe shteibel. It's the Yerushalmi version of Shomer Shabbos in Boro Park.
2- Kikar Shabbos. The intersection the brings five major streets together (Me'ah Shearim, Yecheskal, Malchei Yisroel, Yeshayahu, and Strauss). Location to many hafganos. Meaningful shopping and restaurants in the surrounding streets.
3- Yeshivas Brisk (Rav Avrohom Yehoshuah Soloveitchik)
4- Probably not much of an attraction anymore, but that was Rav Dovid Soloceitchik's house. Until last month, you were able to walk up and peak in the window to see him.
5- Har Tzvi. A convenient shteibel that gives you a glimpse of Yerushalmi life while being new enough for spoiled Americans. Incidentally, the two sides of the shul feature "mens" and "womans" passing signs.
6- Mir Yeshiva. There are a few buildings on the block. You may want to ask some of the American bochurim on the street where you can find Rav Asher Arieli, or any of the other gedolei Torah that sit in the various batei medrash there. Just walk in quietly and watch them learn.
7- The hardcore Me'eh Shearim residential neighborhood. Not much American-geared attractions here. Just crammed housing and Yerushalmi boys running around.
8- Benny's Supermarket. You can find many American style products here. This is just one of the few stores in the area that serve the tourists and American bochurim who are in the many diras in the surrounding blocks.
ETA: There are numerous other gedolim who live in small, nondescript houses on this map. Rav Gamliel Rabinowitz, Rav Yaakov Moshe Schechter, etc. If you are interested in visiting any, post and I'm sure there are DDFers who can direct you with an exact address.