oh man! i could go on and on and for days and days about music from the 50s and 60s... i don't even know where to begin though!
some of my favorite artists from that era:
Frankie Valli and the Four Seasons
Dion and the Bellmonts
The The Platters
The Crew Cuts
Late 1950s to late 1960s Miles Davis. Particularly his album Kind Of Blue. Not that his earlier work wasn't amazing, but there's something about that "cool" jazz that started being introduced in the early 50s that's just simply amazing.