The Velvet Underground & Nico ~ The Velvet Underground
American Beauty ~ The Grateful Dead
Cheap Thrills ~ Big Brother & The Holding Company (Janis)
Sounds Of Silence ~ Simon & Garfunkel
These are the huge 4 albums I can think of you should definitely dig into if you're getting into sixties music. Especially Simon & Garfunkel if you're into the acoustic/electric folk-rock sort of thing of Surrealistic Pillow. Janis is a little more hard-rock, the Velvets are kinda... out there, and the Dead album has a sort of folk/country/extremely beautiful music too good for words twist.
After Bathing at Baxter's, Crown Of Creation, and Volunteers by the Airplane are also definite must-buys. I would start with Crown of Creation, because it's the most accessible, in my opinion. It also spotlights Grace (Three leads instead of her usual two) and we could all use some more Grace.
Hope you enjoy getting into sixties music. It's really great.
"War's good business, so give your sons
But I'd rather have my country die for me" ~ Grace Slick, Rejoyce 1967