Doubt it still works but you used to be able to zone into http://www.wowhead.com/the-obsidian-sanctum as a low level and have another character clear. The XP was nuts... But I think its been hotfixed.
Otherwise I spec into tank or healer and just dungeon grind with full looms, it's very quick. When you get to Blackrock Depths you can Q for that first BRD option (can't remember what it's called) but q it, take tunnel to grim guzzler, jump down, kill fire boss, turn around and clear up the ramp. Dungeon completes in like 5-10 mins, very quick. Rinse repeat, do that until lockout.
If you have someone to clear for you, any fast dungeon works well for farming the "dungeon complete" XP, you dont even have to be inside until the last boss. If you get your hands on an XP increasing buff, you can log out outside the dungeon (in party) until the last boss, log in, enter, have them kill boss (and get XP), leave and log out (remain in party for reset). Rinse/repeat and get 10-15 completion XP from your 15 minute XP buff.
Planning ahead helps with that... you can outlevel a dungeon before the buff timer is up and waste some XP in transit to another. Best for big gaps or adjacent dungeons. Or entire expansions. The nexus is a good one to zoom right through LK to 68-79 for you, BC requires some travel in my experience. If you arent using XP buffs, then it doesnt matter, still great XP for little effort.