37-38
Dustwallow Marsh! Lots of good quests to do. Heck, you could probably even get close to 39 if you havn't already quested here before. Grab every quest in the zone (there are some scattered in the marsh at different places, and a few escorts) and get to it!
38-40
Finish all STV and Booty Bay quests. If your on a PvP server, do most of them with some other people that are in the area to help avoid possible gankings (which will slow your time down). Don't leave STV/BootyBay until your 40. Toward the end of level 39, you will probably run out of good quests. I suggest grinding the last of it or doing a run of SM or RFD.