TOD:
Adding to music groups already mentioned:
The 1960s New York Philharmonic under Leonard Bernstein's baton was the best American orchestra
LOVE (Arthur Lee, Bruce Botnick)
Bob Crewe Generation
Jimmy Webb (not really a group, but an idiosyncratic 60s song writer)
Mason Williams
Bob Dylan (but, of course: more of a Bob post-motorcycle accident fan)
Vince Guaraldi Trio
Rod McKuen
Herb Alpert and The Tijuana Brass
Burt Bacharach (as a solo act as well as a song writer/composer)
Count Basie and his orchestra (Basie had a great lineup in the 60s and had some great arrangers, including Neal Hefti)
Anita Kerr
Glenn Yarborough
(The aforementioned) Petula Clark, particularly "Sign of the Times" and "Downtown", great collaborations with
Tony Hatch
Paul Mauriat
Franck Pourcel