This is the oldest surviving Synagogue in Washington, DC, having been built in 1876 - its descendent is in Cleveland Park, very close to where Palena was.
I'm not even certain which neighborhood the Lillian & Albert Small Jewish Museum resides in, but it has moved more often than the Cape Hatteras Light (really, it has).
"The Little D.C. Shul that Could" by Raquel Wildes on tabletmag.com
This may not be as "obligatory" as visiting the U.S. Holocaust Memorial Museum, but it's a quick visit, has easier access, and is a whole lot less depressing.
I believe the Synagogue itself is temporarily closed, but there are guided tours, as well as sidewalk chats.