Yes, they did improve but continued to have their ups and downs. A process of re-establishing good relations begun almost immediately after Stalin's death, but both sides approached it rather carefully. Yugoslavia had no intentions of either implicitly or even less so explicitly recognizing the role of Soviet Union as the leading socialist state and therefore its rights to intervene or even comment on socialist development in other states. Soviet Union for its part was ready to blame the split on Beria (and after 1956 Khrushchev's "secret speech" on Stalin himself), but couldn't acknowledge Yugoslav position that it was a fault in system itself. Also, Soviets were somewhat worried that Yugoslavia might set an example for other socialist states. Khrushchev did visit Yugoslavia in 1955, Belgrade declaration officially ended the conflict. But soon after, with Soviet intervention in Hungary tensions were renewed, though briefly.

In general, that is how relations remained, friendly but guarded, improving and deteriorating depending on particular circumstances. Critique of Soviet system remained an important part of Yugoslav socialist identity, and doubts about how socialist Yugoslavia really was remained important for Soviets.

As for USA, as early as 1950 a policy of "keeping Tito afloat" was accepted. The goal was to preserve Yugoslavia as a socialist state independent of Soviet Union, as a potential example for others - more or less exactly what worried the Soviets. Those relations also had its ups and downs, but the minimum of keeping Yugoslavia as socialist alternative was kept.

Importance of Yugoslavia stemmed from it as a potential, often actual, meeting place between two blocks, economic, cultural, academic, etc. For example, university courses in Dubrovnik were one of not too numerous places where students and faculty from both blocks regularly met. With the development of Non-aligned movement, Yugoslavia could also be useful for both superpowers as an indirect contact towards the Third world, as it was mainly distrustful of both superpowers.