If the question is, "Do other countries have secret military and/or research sites that they don't let people into?", the answer is, "of course." The USSR had many "closed cities" centered around secret research, like Arzamas-16 (nuclear research), Chelyabinsk-40 (nuclear production), Sary Shagan (antiballistic missiles), and individual labs like "Military Compound 19" in the closed city of Sverdlovsk (biological warfare). The UK had places like Aldermaston (nuclear), Sheffield (nuclear), and Porton Down (biological and chemical warfare). Israel has Dimona (nuclear). Any state that develops WMDs is going to have secret sites, or sites with secrets, anyway.

If the question is, "do other nations have sites that are associated with ideas about aliens?", I don't know that. I have the impression that Sary Shagan was associated with lots of mysterious things because of their work with lasers and radar, but I don't know if there was ever a Soviet rumor mill about it the same way there is for Area 51.

If the question is, "do other nations have secret sites that are known to be secret and have been considered pretty mysterious?" — some of the above sites had "mysterious" reputations during the Cold War and even today (e.g. Porton Down), though some are just "known secrets" in the same way that Area 51 is (it is paradoxically common knowledge that it is a secret site).

Not sure if that clears is up — the question is a little ambiguous.