Alliance: Westfall, Duskwood, Ashenvale.
Horde: Silverpine Forest, 1k Needles, Stonetalon.
You must bear in mind though that stories in Vanilla aren't nearly as linear or self-contained as in post-Cata zones. My favourite is the old version of the You Are Rakh'likh, Demon quest. Oh, and The Missing Diplomat isn't bad at all, although it's Ally-only.