Jewish Autonomous Oblast
This rarely visited province was established by Stalin as an attempt to boost the population of the Soviet Far East as well as to appease Zionist movements within the USSR (which were contradictory to Soviet dogma). The Oblast's "Jewish" status has led to some odd Soviet-Jewish art, such as the menorah monument in the city center, but did not lead to mass Jewish immigration - Jews constitute only about 2% (although there are some reports that is is up to 16%) of this region's population. Some, however, did heed the call of a Siberian Zion, including the Californian family of Mary Leder, author of the fascinating memoirs "My Life in Stalinist Russia."  Potential visitors should definitely try to get a hold of the recent documentary film, L'Chayim, Comrade Stalin, about the history and modern times of the Jewish autonomous oblast.
Yiddish shares official status with Russian, but you are unlikely to hear it aside from a synagogue visit or on the one Yiddish radio station. Ethnic Russians constitute 90% of the population, Jews only about 2% (although some report that is up to 16%), and everyone communicates in Russian.