I feel being asian limits my opportunities in some ways, I remember Martha (first black companion in Doctor Who) saying when they travelled to Shakespearean England and the Globe Theatre she was worried she'd be carted off as a slave, but the Doctor's a boss and would protect her.
So I'd probably say the Swinging 1960's because of the genesis of Modern Rock and Roll from the Beatles and Woodstock, etc.
I voted 50s-60s, but it was a close-run thing with 30s-40s. I tend to watch movies and listen to music from the 30s-50s, and I like books from that time too, but I also have a habit of dressing 50s-60s... so lack of war-time won out. All the periods would be fascinating, but the 20th century is more confortable.