You'll have to wonder around your own starting area and do the quests you're given when you're in this level range. It's important that you don't switch your starting area (for example, a dwarf priest being portalled to Exodar to quest there) because you'll get your racial specific spells and class specific quests in that area and you might not want to miss them.
Once you hit level 15 or so, you can venture on in the Deadmines and Ragefire Chasm (if you're Horde, since the entrance to Ragefire Chasm is inaccessible for Alliance characters). A few Deadmines and/or Ragefire Chasm runs combined with the quests inside these dungeons can easily boost you to level 17-18 and you can start looking for a group to Wailing Caverns. Since the Wailing Caverns is more accessible to Horde players, being located in the Barrens, Alliance priests might want to get to level 20 grinding or questing. World of Warcraft Priest Leveling Guide - Levels 21-30
At level 21 you're still getting good experience from the Wailing Caverns and even from Deadmines, but it's just a tad early to go to a higher instance such as Shadowfang Keep or the Stockades if you're an Alliance priest. I recommend that you try out questing and grinding a few more levels in areas near your starting location. For Alliance priests, you should try out Redridge Mountains (20-22), the Wetlands (22-23) or Ashenvale (23-24). Horde players will be able to quest in several parts of the Barrens (20-23), Ashenvale (23-24) and even start questing in Duskwood (20-30).
When you're level 24, the grind is over and you're ready for a new set of instances. Shadowfang Keep (22-30) in Silverpine Forest is slightly harder to get to for Alliance priests but it offers some great drops for cloth wearers and is well worth it. Blackfathom Depths (24-32) in Ashenvale is slightly harder and longer, but it's rather fun and has some nice drops at that level. Finally, just like level 14-18 Horde players had Ragefire Chasm all to themselves, level 24-32 Alliance priests have The Stockades in Stormwind to quest and instance in.
And if you're tired of Blackfathom Depths, The Stockades and Shadowfang Keep by level 28, you can try out Razorfen Kraul (26-30) in the Barrens, although Alliance priests will have a harder time getting to that area and finding a party for this instance. However, the same goes for Horde priests that want to do Gnomeregan (28-32) which is quite an adventure for any Horde priest to get to
Levels 31 to 40 are a bit hard for a priest, regardless if you're Alliance or Horde. You don't have a mount yet and it's difficult to travel around the World, you need to gather up money for your mount at 40 so you can't really spend on gear or professions and you will find yourself leveling in contested areas that are gank heaven if you're playing on a PVP server. And as a priest, even a shadow one, getting ganked is something you'll get used to over time.
So watch your step when you're questing around the Hillsbrad Foothills, Arathi Mountains, Stranglethorn Vale, Dustwallow Marsh or Desolace. Of these 5 31-40 questing areas, Hillsbrad Foothills and Stranglethorn Vale are the hardest for a priest, as PVP is right at home here (and let's be honest, before you get Shadowform it's hard to hold up in PVP as a priest). Badlands and Swamp of Sorrows are roughly the same level, but they don't have as many quests as the other areas.
Fortunately you also have several new instances with loads of quests to go through: The Scarlet Monastery, with its 4 sub-instances (Scarlet Graveyard, Scarlet Library, Scarlet Armory and Scarlet Cathedral, in order of difficulty) is a great place for priests to gear up (especially the Library and Cathedral) and Uldaman at around level 38 (if you have a higher level, good group). As an Alliance priest, I would skip Razorfen Downs as it is hard to get to without a mount, doesn't offer a lot of good cloth drops and it's hard to find a group for. As a Horde priest, Razorfen Downs is a good alternative for when you can't find Scarlet groups, or if you just want 1-2 runs to do the quests inside there.
World of Warcraft Priest Leveling Guide - Levels 41-50
Finally, Shadowform! And a mount, hopefully, if you raised the money for it. Finally we can /gloat at those silly druids and their catform or those damned shamans and their ghost wolf. But don't gloat too much, since there's a lot of questing and instancing to be done (less grinding fortunately) at this level range.
I've swept through these 10 levels when leveling my shadow priest, simply by doing the quests in Tanaris (lots of nice quest rewards for priests here), Searing Gorge (lots of quests, small zone, easy experience) and some in Hinterlands and Blasted Lands. The best part of this level range however, is that you can finally get to do some real instances as a priest, with boss encounters where you don't doze off in your chair.
The last boss in Uldaman is a challenge for a 40ish priest (watch those adds!) and at 46 you can start getting groups for Maraudon, which is a large instance with numerous quests and a lot of superb drops for both shadow and holy priests. If you have a good group you can also try Sunken Temple at level 48, but people seem to hate this instance and it's a bit harder to find a group for it.
World of Warcraft Priest Leveling Guide - Levels 51-58
Before The Burning Crusade, this was one heck of a grind. Fortunately, now you can start questing in Outland at level 58, so the grind in Azeroth is a tad shorter. I would recommend Felwood and Un'Goro for questing and grinding your first levels, but on a PVP server you might run in trouble, as these two areas are usually very populated (people grinding, leveling, questing, etc). Un'Goro offers a lot of quests and it's a smaller area, but there's a lot of annoying patrolling elites roaming around (bonus for Night Elf priests that can Shadowmeld).
The Burning Steppes has a lot of humanoid mobs that are relatively easy to kill, which is good for a priest with tailoring, since a lot of Runecloth will drop and you'll be able to make yourself some nice new stuff. And of course there's the Eastern and Western Plaguelands but since most of the ghosts, ghouls and whatnots there are resistant to shadow damage, it's a bit of nausea for a shadow priest so I prefer Winterspring or Silithus anytime.
As far as instances go, Sunken Temple, Lower Black Rock Spire and Scholomance should be your ramp to level 58, when you can enter the Dark Portal. Woohoo!
World of Warcraft Priest Leveling Guide - Outland Outland areas offer a visibly larger quantity of quests per area, which makes earning experience an ok task. Here's how I leveled my priest in Outland:
World of Warcraft Priest Leveling Guide - Levels 58 and 59:
Easier quests around the Dark Portal and from Honor Hold/Thrallmar, as well as occasional Stratholme runs back in Azeroth did the trick to gain these two levels.
World of Warcraft Priest Leveling Guide - Level 60 and 61:
You can take up most of the camp quests in Hellfire Peninsula at level 60 and you can start getting Hellfire Ramparts groups. Try to do grind Hellfire Ramparts as much as possible, since it's a fast, relatively easy instance, with good priest drops. You'll also need Honor Hold/Thrallmar reputation and it's better to get to honored through instancing first and save up the reputation you get from quests for getting to revered.
World of Warcraft Priest Leveling Guide - Level 62:
Blood Furnace runs, plus Temple of Sha'naar/Falcon Watch quests.
World of Warcraft Priest Leveling Guide - Level 63:
You're probably done with most of the quests in Hellfire Peninsula, so go to Zangarmarsh and focus on the Cenarion Expedition quests. At level 63 you can also get a group for the Slave Pens and Underbog, both instances having some great blue drops. If the Underbog is a bit too hard for you for the moment, Slave Pens and the plethora of quests around Zangarmarsh should provide the necessary boost to 64.
World of Warcraft Priest Leveling Guide - Level 64:
By the time you're 64, you can move on to the Western part of Zangarmarsh for the Orebor Harborage/Zabra'Jin quest hubs. The Blood Furnace and the Slave Pens become slightly easier now, which should provide you with faster runs (but less experience). You can also start doing the Underbog and even Auchenai Crypts in Terokkar Forest.
After you're done in Zangarmarsh, the next logical area is Terokkar Forest and the city of Shattrath. Terokkar Forest is great to quest in as a priest, since the mobs drop a lot of netherweave cloth and there are also a lot of spiders around that will drop the silk needed in your tailoring recipes. But after you're done with the quests in Terokkar Forest, you'll have the option to go in either Nagrand or Blade's Edge Mountains. I personally prefer Nagrand as a priest, due to the fact that it's easier to get around with and I get mob-ganked in Blade's Edge way to often to make it a fun leveling area. Nagrand should provide enough quests for you to get to level 67 and you'll also get a lot of motes/primals from the elementals there that you can use later on in crafting or buying epic set gear.
