In the final opening quests you're forced away from Gilneas for reasons I won't mention. (Won't spoil the entire plot for you.) Now you're level 12 and in Darnassus, free to continue leveling anywhere. At first I decided to follow the natural chain of events and quested in Darkshore. This zone was greatly changed by the Cataclysm, with the main town of Auberdine completely destroyed.
The questing experience here was greatly improved, with far more quests available than before. Several of them make use of phasing and the new indicator arrows to point out certain quest objectives. I did around 20-30 quests here to find I was a bit too high level for everything in the zone so I wasn't getting the best EXP possible. At level 15 (after making good use of the dungeon tool just unlocked) I decided to go elsewhere. The human low level zones (Westfall - Stranglethorn Vale) are my favorite so I took the boat to Stormwind and ran to Redridge Mountains.
Right at the western edge of the zone there was a new guard tower, with several quests available before even reaching Lakeshire. Upon finishing them and reaching Lakeshire, the first difference I noticed was the bridge. Currently one of the NPCs on live is always talking about finishing construction and here it's complete. Once again, many more quests are available here and go more smoothly than before. The questing experience seems to have been overhauled completely throughout Azeroth. Being that I like this zone, I quested here until 20 or 21 though I still seemed to level past the zone before completing much of the quests.
It's worth noting that about this time I finally learned about the new hierloom items, the head and cloak slot ones. Apparently (at least in that build of the beta) they were all available from the guild vendor for free. With those I got a 15% experience bonus that makes the levels fly by, especially since being a tank means I can get in dungeons quickly.
There were other interesting items the guild vendor had like new pets and the Dark Pheonix mount, but the items were all placeholders with no actual effects yet so no idea as to the coolness or the cost of them, though I'm sure they will all require some amount of guild reputation.