I love the Byrds. They're one of my dad's favorites and I grew up listening to them. Some good albums to check out:
Sweetheart of the Rodeo, Ballad of Easy Rider, Notorious Byrd Brothers, Untitled, and Doctor Byrds and Mr. Hyde.
If you like the Byrds check out The Flying Burrito Brothers. It was a group that Gram Parsons and Chris Hillman formed after leaving the Byrds. The first album Gilded Palace of Sin is great. Gram Parsons solo stuff is awesome too.