Every item listed that drops from a quest will have an Alliance and/or Horde quest link. If you don't see an A or H after the stats, then your faction can't get the item.
Chest: Sacred Feather Vest (15 sta, 13 int, 10 spi, 14 crit, 42 dmg) [A H] is the reward from an easy L58 solo chain out of Hellfire Peninsula that can net you a chest piece you won't be replacing for quite a while. If you already did this quest and chose a different reward, you can snag a L60 Omenai Vest (28 sta, 19 int, 22 dmg, 8 mp5) [A] quest chain out of the Temple of Telhemat in Hellfire. Alternatives at higher levels: a L67 Nether Vest (28 int, 17 crit, 34 dmg) [A/H] out of Netherstorm or pick up L68 Grom'tor's Friend's Cousin's Tunic (15 sta, 21 int, 46 dmg) [A/H] which is the 11th step in a very long chain that gets you attuned for Tempest Keep and Mt. Hyjal.
If you are Leatherworker, you've hit the jackpot for once. The L65 Living Crystal Breastplate (23 int, 17 spi, 29 dmg, 55 heal) isn't bad if you're pulling double duty with healing and dps'ing, but then there's the L70 Windhawk Hauberk (24 sta, 25 int, 25 spi, [BS YS BS: 4 agi], 16 crit, 28 dmg, 35 heal). It's the best non-raid chest piece in the game for Balance druids. Only craftable by Tribal Leatherworkers and not tradable. Finally makes Leatherworking look like a viable profession.
As for instance drops, keep an eye out for the L63 Tunic of the Nightwatcher (27 sta, 21 int, 18 spi, [RS YS BS: 2 mp5], 26 dmg) from Swamplord Musel'ek in The Underbog (17.5% drop) or the L70 Starry Robes of the Crescent (23 sta, 30 int, 24 spi, 19 crit, 39 dmg) from Pandemonious in Mana-Tombs (12% drop.)
Legs: Nature-stitched Kilt (19 sta, 19 int, 12 spi, 23 dmg) [A H] are from another easy to pick up quest in Hellfire Peninsula. You cab grab them as early as L58 if you want. You can also pick up Explorer's Leggings (23 int, 22 spi, 26 dmg) [A/H] from an escort quest in Zangarmarsh at L60, Leggings of the Third Coin (34 sta, 26 int, 12 crit, 32 dmg, 4 mp5) [A/H] from a L64 quest that starts in Auchidoun (Terokkar Forest) and ends in Auchenai Crypts or Leggings of Concentrated Power (34 sta, 23 int, 23 spi, 27 dmg) [A/H] in Netherstorm at L67.
On the kill them and loot them side, Moonchild Leggings (26 sta, 20 int, 19 spi, [RS YS YS: 2 mp5], 21 crit, 23 dmg) drop from Boggrok in Heroic Blood Furnace (16% drop, req L70).
After the Nature-stiched Kilt, you may just want to hold out for Haramad's Leggings of the Third Coin (29 int, [YS YS RS: 5 dmg], 16 crit, 27 dmg) [A/H]. They are easily obtainable from a quest that asks to kill the end boss in the Mana-Tombs, which you are going to do anyway. And this nets you the 3rd best pants in the game for Balance druids at L64.
Then there are the leggings that beat even raid level pants. The Alliance version is the Kurenai Kilt (11 int, [RS YS YS: 2 mp5], 18 crit, 44 dmg) and can be obtained from gaining Revered with the Kurenai. The Horde version is Tempest Leggings (11 int, [RS YS YS: 2 mp5], 18 crit, 44 dmg) and has the exact same stats, but is obtained from getting Revered with the Mag'har.
Helm: Moonkin Headdress (30 sta, 20 int, 20 spi, 19 crit, 23 dmg) [A H] is a good one to get off the bat. Head into Hellfire Ramparts. An Ominous Letter has a 33% to drop off the final boss. From there you can turn the letter in and get the quest for this helm. Head into The Blood Furnace to collect the drops.
There isn't much after that until the higher levels, then you have a number of options. Quest rewards include Circlet of the Starcaller (27 sta, 18 int, 17 spi, 18 crit, 47 dmg) [A/H] from a L70 Elite quest out of the Netherstorm that may be done solo by some classes and Mooncrest Headdress (16 int, 21 crit, 44 dmg) [A H] from the fifth of seven quests in a L69 Shadowmoon Valley chain.
Other high level options include Moon-Crown Antlers (25 sta, 31 int, 20 spi, 16 hit, 40 dmg) from Captain Skarloc in Heroic CoT: Old Hillsbrad Foothills (10% drop, req L70) and L66 Exorcist's Wyrmhide Helm - (35 sta, 16 int, [MS: 2 dmg], 10 res, 34 dmg) that costs 18 spirit shards from either Alliance-based Spirit Sage Zran and Horde-based Spirit Sage Gartok. With its high resilience and armor, it may only appeal to Balance Druids that like to off tank or main tank. Spirit Shards drop from bosses in Auchidoun instances while your faction controls the PvP objectives in Terokkar.
You can also hit the Auction House or your guild crafters for L69 Tailoring: Stylin' Jungle Hat (24 str, 24 agi, 24 sta, 24 int, 10 mp5, 19 dmg) or the most awesome L70 Windscale Hood (16 sta, 18 int, 35 crit, 41 dmg, 14 mp5) which will cost someone a Primal Nether.
At the end of the day, the best non-raid Balance helm currently in the game is Druidic Helm of Second Sight (12 sta, 15 int, [YS BS BS: 5 dmg], 24 crit, 35 dmg, 4 mp5) [A H]. Alliance and Horde have different routes in this chain, but end up with same sweet reward.
Shoulders: The earliest TBC Balance shoulders you can get are Elekk Hide Spaulders (12 int, 16 spi, 28 crit, 25 dmg) [A/H] from a L63 quest out of Terokkar. After that you can either pick up Netherfused Pauldrons (21 sta, 23 int, 20 spi, 28 dmg) [A/H] from a L67 elite chain in Netherstorm or the Lunar-Claw Pauldrons (23 sta, 26 int, 17 spi, 29 dmg) that drop from Mechano Lord Capacitus in The Mechanar (either Normal or Heroic mode, 16% drop, L70).
If you don't mind the lack of STA and low INT, the Elekk Hide Spaulders may be the way to go with it's high crit and spell damage until the next expansion.
Bracers: The first bracers you can get out of Outlands come from Zangarmarsh at level 60. Alliance toons get Explorer's Bands (12 int, 12 spi, 14dmg) [A] and the identical Horde counterpart are Bog Walker's Bands (12 int, 12 spi, 14dmg) [H]. The only other early option is Moonstruck Bands (16 sta, 11 int, 11 spi, 13 dmg) [A/H] from a L62 one step quest to kill an easy solo mob in Terokkar.
At higher levels, available upgrades are either Mana Infused Wristguards (12 sta, 8 int, 7 spi, 25 dmg) [A/H] from a L67 Netherstorm quest that has a few prereqs or Moon-Touched Bands (17 sta, 20 int, 12 spi, 21 dmg) that drop from The Maker in Heroic Blood Furnace (15% drop, req L70.)
The last option are the best bracers in the game (including current raid drops). It's the L70 Tribal Leatherworking only Windhawk Bracers (21 sta, 16 int, 6 spi, [YS: 2 agi], 14 crit, 15 dmg, 29 heal). Almost makes me want to take up Leatherworking again to be able to wear these. Almost...
Gloves: Early on there are quite a few options to run with. You can have L61 Wild Dreanish Gloves (13 agi, 13 str, 18 sta, 12 int, 14 dmg) made for you by a Leatherworker or quest for either L63 Gloves of the Afterlife (18 int, 17 spi, 21 dmg) [A/H] in Terrokar or L64 Clefthoof Gloves (24 sta, 16 int, 16 spi, 19 dmg) [A/H] by killing a gazillion Clefthoofs, then go kill some more. And then go kill the king of the dung droppers.
In mid-levels, you can look forward to Miner's Gloves (10 int, 15 spi, 30 dmg) [A] at L65 in the Blade's Edge, Nether-Rocket Gloves (16 sta, 11 int, 10 spi, 33 dmg) [A/H] at L67 in Netherstorm, L65 Netherhide Gloves (11 int, 16 spi, 33 dmg) [H] out of Blade's Edge if you can kill a L68 non-elite dragon or L67 Harmony's Touch (18 sta, 16 crit, 33 dmg) [A/H] from a Netherstorm three step quest.
At L70 there's Grips of the Lunar Eclipse (23 sta, 25 int, 18 spi, 28 dmg) Lieutenant Drake, Heroic Old Hillsbrad 12% drop L70.
However the second best gloves in the game have a 1 in 5 chance to drop from Hungrafen in The Underbog and you can wear them at level 63: Starlight Gauntlets (10 sta, 21 int, 8 spi, [BS BS: 5 dmg], 25 dmg). If you get a pair of these early on, like I did, you won't have to worry about this slot until the expansion hits.
End Notes: If you have a gap in your armor and can't get the next upgrade, you can always hit the AH and do a search for "of the invoker" or "of the sorcerer" leather. Good fill-in armor for cheap.
Much of this information was culled from this phenomenal thread on BC Balance Loot on the official forums. Check it out if want to learn more about balancing +hit, +spelldamage and +crit gear. There is also a great Balance FAQ starting with post fourteen.
This is it for today. In two weeks I'll be back with listings for the remaining slots. And after that, I'll cover restoration druids.
I'm sure I might have missed a piece or two. If you have any recommendations, be sure to list them below.