The Alliance leveling zones that Cataclysm has brought to the World of Warcraft universe are all shared with the Horde ones. Therefore, if you play on a tough PvP server you should be prepared for all the random battles for quests, bosses, areas or resource with the opposite faction players.
There are 5 major zones: Mt. Hyjal, Vashj'ir, Deepholm, Uldum and Twilight Highlands. I'm going to say a few words about these zones, and about the advantages and disadvantages of leveling through each one of them.
Mount Hyjal
This is one of the starting zones for the Cataclysm content. It's actually the zone that you should choose to level up from 80 to 82. Although the terrain isn't that accessible, with at least a normal flying mount and the Flight Master's License you will be able to easily move from a quest hub or area to another.
Mt. Hyjal is the home of the faction Guardians of Hyjal, and by completing quests here you will gain reputation with this faction. By completing all the quests in this zone you will become revered with this faction and gain access to the caster helm enchantment. The quartermaster is located at Nordrassil.
Vashj'ir
This is a completely sunken world, and most of the quests here will be underwater. As you start this zone, the first quests will grant you underwater breathing, and later on, you will receive a fast underwater mount. However, this zone isn't that viable for leveling because you have to cover wide area from a quest hub to another.
The quests here are catchy and if you would like to follow a rich storyline, Vashj'ir is the zone that you should choose to level up from 80 to 82.
Some of the quests in Vashj'ir grant reputation with the Earthen Ring faction. By completing all quests in Vashj'ir you will become honored with this faction. The main camp of the Earthen Ring where you can also find the quartermaster is in Silver Tide Hollow, in Shimmering Expanse.
Deepholm
This is the third area of Cataclysm, meant for players in a level range of between 82 and 84. This is one of the Horde and Alliance leveling zones that Cataclysm has placed in the Elemental Plane. It's the home of the Therazane faction, which you can unlock only after you complete quite a big chunk of quests here. The Therazane Throne where the quartermaster can be found is in the northern part of Deepholm. The main quest hub is in the middle of the zone, at the Temple of Earth.
While leveling in this area you might want to keep an eye out for Aeonaxx, a very nice rare spawn drake, which drops the Reins of the Phosphorescent Stone Drake - a super cool flying mount.
Uldum
If you liked the Indiana Jones movies you will surely like this zone. The main quest line involves helping out the notorious archaeologist Harrison Jones to elucidate the mysteries of the zone.
The main quest hub is also in the center of the zone, at Ramkahen, the home of the dominant faction of this zone. As you may have guessed, most of the quests here grant you reputation with this faction.
When it comes to leveling through this zone, you should at least complete some of the quests here until you unlock the portal to Stormwind city. The zone is highly accessible, but also very wide and without a fast flying mount you will probably waste some time here.
Twilight Highlands
TH is the exit zone for the Alliance leveling zones that Cataclysm has put into World of Warcraft. There are many quests here, including the arena 5-quest chain - Crucible of Carnage. This should definitely be your questing destination for level 84-85.
The main faction that you should unlock here is the Wildhammer Clan, with their settlement at Thundermar, where you will also unlock several daily quests.
That's about it when it comes to the presentation of the five Cataclysm zones. Here two general paths that you can follow while leveling through the Cataclysm zones.
1. Hyjal, Deepholm and Twilight Highlands. If you use all the Heirlooms and you benefit from all the XP bonuses possible. Also, to follow this path you should complete all the quests in Hyjal and Deepholm, which will take you to level 84.
2. Hyjal or Vasj'ir, Deepholm, Uldum and Twilight Highlands. The normal order for questing here, in case you don't have too many XP bonuses.
Although these 5 zones are the last zones introduced to the game, you should know there are many other Alliance leveling zones Cataclysm has changed so far.
In any case to level as fast as possible from 1 to 85, it's best to follow a well-determined quest path, broken down step by step. Best solution for that would be an Alliance leveling guide.