The Austrian-American logician who became a close friend of Einstein at the Institute for Advanced Study was Kurt Gödel.
Gödel was born in Brünn in 1906, then part of Austria-Hungary, and became one of the twentieth century’s most important mathematical logicians. His incompleteness theorems showed that sufficiently powerful formal systems contain true statements that cannot be proved within those systems, transforming the study of mathematics and computation.
Gödel joined the Institute for Advanced Study in Princeton and developed a close friendship with Einstein, who was also a faculty member there. The two often walked together between the Institute and their homes, discussing general relativity, philosophy, mathematics, and the nature of time. Einstein reportedly said that he went to the Institute partly for the privilege of walking home with Gödel.
Gödel also made a major contribution to physics: in 1949 he found an exact solution to Einstein’s field equations describing a rotating universe with closed timelike curves. The other options are notable scientists, but none fits the question: Dirac was British, Weyl was German, and von Neumann was Hungarian-American and a mathematician and polymath.