There are several drops in The Nexus, the first dungeon available in the Borean Tundra zone (technically it's in Coldarra, home of Azure Shields and lots and lots of blue dragons) is a lore explosion of dragons at war over magic. But we're more interested in the loot available. Because I am a heartless mercenary who will kill whatever I have to for loot, yes I am, and I don't deny it.
For starters, there are several quests that ask you to go into the Nexus. Prisoner of War is the end of a fun Coldarra questline that gets you up close and personal inside how dragons wage war (they don't mess about) and yields three rewards, all of which may be of interest to a shaman. The Shroud of Fluid Strikes is aimed at melee and has decent AP and haste, while both the Mantle of Keristrasza and Cloak of Azure Lights could appeal to your caster/healer shaman. (I would probably get the Cloak of Azure Lights to pull double duty for me, as spirit isn't as important to shamans as it is to other casters.)
Another quest, The Quickening, does not ask you to cut off the Kurgen's head. It does, however, offer up a nice pair of spell power boots, the Spiked Treads of Mutation, which seem aimed to restoration with the MP5 and the lack of crit. But they'll certainly work for elemental shamans as well. There's also the Treads of Torn Future if you're hurting for enhancement boots and don't mind leather. Finally, the quest Postponing the Inevitable offers up a nice pair of enhancement gloves, the Bindings of Sabotage.
As for drops in the instance themselves, there are four that stood out to me: the Band of Glttering Permafrost which has every stat a restoration shaman would want. The Belt of Draconic Runes is leather, but could certainly serve for either elemental or restoration (really, while some gear may be more ideal for one spec over the other now, most gear that could serve for one spec works for the other thanks to the unification of spell power - I'd always give the nod to spell hit and spell crit for elemental but it's not as big a deal anymore). The Cleated Ice Boots are your enhancement booties, (so I'd try for these rather than taking those leather quest boots) while the Gauntlets of Serpent Scales are pretty solidly aimed at elemental shamans but could serve a restoration shaman. (Some enhancement might even want them for the AP from int, although almost certainly the Bindings of Sabotage would serve them better.)
General Quest Rewards
Listing every green drop that could benefit a shaman would take us an easy 1000 words just in Borean Tundra alone, so I'll just focus on a few exceptional rewards and move on.
From the Horde quest Hellscream's Champion (and its Alliance brother, Last Rites), you can find several pieces that will serve shamans. If you are enhancement and haven't gotten a badge weapon or a PvP weapon yet, the Borean Smasher is as good as a Prince Malchezaar/Heroic Magister's Kael'Thas drop. For our caster/healer contingent, there are two staves to choose from, the Tower of the Infinite Mind (DPS flavored, in my opinion) and the Staff of the Purposeful Mendicant. I generally prefer weapon/shield combos myself, but these are some pretty nice sticks.
If you're in the mood to kill a guy you might remember from laying on his back bemoaning a scratch, then you can get some good rings for it. The Band of Indignant Rage is a pretty sweet deal for an enhancement shaman, especially since we lost our major hit talent in restoration. The Band of Wholeseome Preservation has every stat I associate with restoration now as well as crit rating for Ancestral Awakening procs (although the crit and spell power aren't exactly bad for elemental) and the Activist's Signet of Blasting has nice stam as well as spell power and haste. Either ring could serve either spec depending on what you wanted to gear for, really.
Finally, if you're an Alliance shaman there's the quest Call to Arms! which, sadly, does not seem to have a Horde equivalent. Boo. Hiss. What it does have, however, are some pretty nice necks. The Chain of the Tolling Bell has hit rating, expertise and AP for you enhancement shamans looking for a solid neck. The other two necks, the Indomitable Choker of Light and the Pendant of Revolutionary Thought, mirror the rings above in that either could work for either restoration or elemental. I'd say I'd take the Indomitable Choker as resto (hit rating isn't that necessary for healing) but either neck could work for elemental, again depending on what your gear priorities are.
The other starting level dungeon in Northrend is full of bloodthirsty giant vikings who worship the Lich King. I recommend doing the Fjord if only to hear the chilling opinion of the Lich King himself about shamanism. As was the case for the Nexus you'll be sent into Utgarde Keep on a variety of quests.
Horde only get the quest A Score To Settle asking you to kill Prince Keleseth. The rewards? The Runecaster's Bracers, with all their spell power and MP5 for the casting shamans among us. Both Horde and Alliance get Disarmament, which its variety of necklaces for shamans. The Razor-Blade Pendant isn't as good as it would have been now that we only get 1 AP per point of STR, but the Amulet of the Tranquil Mind isn't bad for a restoration shaman and the Necklace of Fragmented Light seems good for an elemental shaman to me. Finally, both Horde and Alliance have a chance to pick up some rings here. The Executioner's Band will serve your enhancement shaman well (my draenei replaced his Karazhan epic with it) while I would personally chose the SIgnet of Swift Judgement for both caster shaman specs over the Ring of Decimation.
As for drops themselves, the Arm Blade of Augelmir is better than the Season 2 PvP weapon and not that far from the badge rewards. And while you're trying to get that for your enhancement shaman don't ignore the Dragon Stabler's Gauntlets, which are comparable to the 75 badge gloves. Even though their leather, the Holistic Patchwork Breeches would work for a shaman, but the real prizes for our caster shaman are Keleseth's Blade of Evocation and the Overlaid Chain Spaulders. Whether you like healing the wounded or causing their wounds, these are nice drops.
General Quest Rewards
What stands out in the Fjord for you to pine for? Well, there's two quest chains that give out a nice assortment of trinkets to look over. Help the Tuskarr out and they'll send you back to Atuik: his rewards consist of a very nice MP5 trinket with a spell power on use, a haste rating/AP trinket, and a haste rating/spell power trinket. I took the MP5 trinket.
If you'd rather assassinate a pirate leader (or are going to do both) there's a crit rating/spell power trinket, an MP5 trinket with a haste rating on us, and an AP trinket with haste rating on use. I took the MP5 trinket again on my orc but went with the AP for my draenei.
There's plenty of green quest rewards comparable to Karazhan gear in the two zones as well, but there's a finite amount of time and space to cover it all, and these rewards and instance drops should at least give you an idea of what to expect next week. Have fun storming the various castles!