Yeah, you'll really only want to do each dungeon once or twice, with as many quests as possible. Dungeons are horrible exp in vanilla.
I've never leveled horde in Vanilla, but for Alliance, I typically do:
-Deadmines (2 quests in elite area outside instance, quest for bandannas, quest for VC head, quest for specklesprocket, and quest chain that starts from the letter VC drops)
-Stockades (various kill quests that you pick up from lakeshire, darkshire, wetlands, etc)
-SM (short quest chain in Desolace that leads to a quest to kill SM Lib/Arm/Cath bosses, really nice quest rewards)
-ZF (almost all of the quests are very close to the instance)
-Mara (again, most of the quests are in Desolace, or near it in Kalimdor)
And from there, you'll be doing the rest of the 50+ instances anyways, for gear.