In a super rush at the moment so can only note a few. Wish we had more time for this as I love 60s music! In fact, it's at the root of why I love Shoegaze music. A lot of very good ones already listed. Sorry if I duplicate. One or two of these might dip into 1970 or so but they fit the mood.
Mystic Eyes - Them (Van Morrison's original group)
Inscence And Peppermints - The Strawberry Alarm Clock
96 Tears - ? And The Mysterians
Wild Thing - The Troggs
Sky Pilot - The Animals
A Whiter Shade Of Pale - Procol Harem
LA Woman - The Doors (Worth it for the intro)
Along Comes Mary - The Association (for mellower moments)
White Rabbit - The Jefferson Airplane
Up Against The Wall Motherfucker! - The Jefferson Airplane (Is that the name of the song? Great protest song.)
White Bird - It's A Beautiful Day
Journey Through The Center Of The Mind - The Amboy Dukes
Hush - Deep Purple (not that Smoke On the Water crap though!)
Society's Child - Janis Ian
As Tears Go By - Marianne Faithful
Gold Finger - Shirley Bassey
Secret Agent Man - Johnny Rivers
Magate Brain - Funkadelic
Lies - The Knickerbockers
My Friend Jack - The Smoke (or maybe the song is called Sugar Lumps)
Almost anything by The Beatles, The Rolling Stones, The Supremes, The Temptations & The Monkees providing you stick with something earlier or, at least, from the 60s itself, especially regarding The Stones.
Because I'm in a rush, I'll just list a few other bands and take it from there. Others will probably pick up my dropped ball.
Donovan
Martha & The Vandellas
The Ronettes
Sam & Dave
Smokey Robinson & The Miracles
The Searchers
Lulu (To Sir, With Love for those graduation moments)
Gary Lewis & The Playboys
Freddy & The Dreamers
Very early Beach Boys
Jan & Dean
The Ventures
The Spencer Davis Group
The Chocolate Watchband
Ultimate Spinach (might get too spacey for you though)
The Electric Prunes
Arthur Lee & Love
The Buffalo Springfield
Janis Joplin (something early with Big Brother & the Holding Company)
The Jimi Hendrix Experience
something from the 1st Terry Reid album
Curved Air (Might be '70 and almost left them off since they might get a little too cerebral but you will be with a bunch of Art students so it could work. One of my very favorite bands from back in the day.)
The Shangrilas (spelling?)
The Isley Brothers
Sam Cooke
Glaydes (K?)Night & The Pips
Sly & The Family Stone
very, very early Pink Floyd
Peter & Gordon
Chad & Jeremy
The Mamas & The Papas
Creedence Clearwater Revival
Ike & Tina Turner
The Crystals
The Marvelettes
The Surpremes (definitely stick with something early)
The Kinks
early Bob Dylan
Iron Butterfly
The Pretty Things
The Left Bank
Don't forget to include somewhere along the line, She Was Just 17 by The Beatles and, even though not 60s specific, Ladytron's Seventeen.
You could end the night on a very moody note with Moon River by Andy Williams.
Oh, and Betty....
HAPPY BIRTHDAY!
Damn, this thread has me intriqued!