A bunch of people are recommending the Churvah... What's so interesting there?
I'll explain why I am so enamored by the Churva, though this reason may not be universally appreciated.
The Old City has unfortunately become almost a tourist center. As most people know, even the Kosel can only really be appreciated at night, when tourists are sleeping and frum people are basically the only one's flooding the holy area. The Yiddish feeling has almost been completely erased from the Old City's outward look, as every landmark and holy site has been overtaken by throngs of camera-toting foreigners or Zionist ideologicals who don't represent the yeshivish mindset.
The Churva should be the quintessential destination of that sort. It's very name and history tell the story of how it was destroyed and then rebuilt - a Zionistic legend, and the impressive, tall structure can impress any sightseer. Indeed, hundreds of tourists pass through it every day.
But...
The tourists cannot enter the bais medrash. They merely peek in from the hallway outside, or ascent to the balconies above and look down at it. In the bais medrash, a mere two minute walk from the kosel, there is a vibrant kollel of yeshivaleit learning, each member involved in a Rashba or lost in a Rav Chaim Brisker. I've personally spent numerous sedorim in the bais medrash while I was learning in Eretz Yisroel, completely tuning out the stream of tourists looking in from the hallway. (There is a back door that goes directly into the Bais Medrash, which the kollel-members use, and I've gotten the combonation when I was there.)
The oasis of pure Torah learning in the epicenter of what has unfortunately become tourist-land is something that has always been so alluring to me. And it is why my Churva recommendation did not say, "visit the Churva," rather, "learn a seder in the Churva."
