There were hot spots all over the place in the Cold War of the 1950s.
Perhaps the most obvious hot spot was in Asia. The decade of the 1950s started off with the Korean War from 1950-3. This was very much a Cold War conflict as it involved a communist country trying to invade a non-communist one. There was also the beginning of the conflict in Vietnam, with the communists ousting the French in 1954.
There were also hot spots in the Middle East. The US helped to overthrow the government of Iran in the 1950s. There was a major crisis in the Suez in 1956. Both of these were linked to the Cold War as well.
These are probably the two hottest spots, but there was conflict in practically every corner of the globe in the '50s.