Its fun to try and think what music really brings back the atmosphere of the sixties but its more difficult than it seems. Not only was there so much good music around but over the decade there were a lot of changes. There was the beginning bit, 1960-1962, which seemed like an extension of the fifties. Then came 1963 and after the Beatles released Please, Please Me British bands dominated the air waves for quite some time, though this overpapped with Tamla Motown, Soul and the protesters like Bob Dylan and Joan Baez. After this, from about 1966, came the American hippie sound with bands like the Doors and Jefferson Airplane and psychedelia on both sides of the Atlantic. In the late sixties, albums seriously took over from the three minute pop song and prog rock arrived just in time for the seventies. Well that's how it seems to me although I have left rather a lot out!
One thing that was interesting about the early to mid sixties were the high profile connections between British bands and some provincial towns. It was not only the Beatles and Liverpool but the Hollies and Manchester, the Move and the Moody Blues and Birmingham and a little later Joe Cocker and Sheffield. It gave those towns a real glamour for music addicts. I still feel excited by St Albans because I liked the Zombies. I don't think there was a Leicester band though-had to wait for Family in the seventies for that.