The Wintergrasp dailies are also an excellent source of Honor and some can be done without actually doing any PvP whatsoever, which is a strange new trend in Wrath of the Lich King, where the PvP side of the game is accessible entirely through PvE. The very first daily quest is self-explanatory -- Victory in Wintergrasp, which requires players to win a battle for the zone. Alliance players get this quest from the Tactical Officer Abrahmis, while Horde players get it from Tactical Officer Kilrath. If you control the zone, these NPCs can be found in front of Wintergrasp Keep, where the Titan Relic is housed. If you don't, they can be found in the landing camps on the East or West.
The quest seems to be currently unavailable in the game, as it has been very buggy and many players have reported not completing the quest even after a victory and having the requisite Rank. I'm certain the quest will return in bug-free form with Patch 3.0.8, if not hotfixed sooner. Completing the quest awards one Stone Keeper's Shard, 13 Gold 23 Silver, and 1241 Honor at Level 80.
No Mercy for the Merciless (A) / Slay Them All! (H)
Just like most quests in Wintergrasp, this is pretty straightforward -- kill 20 members of the opposing faction. Unlike other Northrend PvP quests, such as the ones in Grizzly Hills, only players and not NPCs will count towards this quest. Because of tagging mechanics, it's best if you do this while in a raid group. Players killed with a vehicle will count, too, so don't worry about taking control of one.
Alliance players can obtain this quest from Commander Zanneth while Horde players can get this from Commander Dardosh. Just like all Wintergrasp NPCs, they will spawn inside the Fortress if your faction controls it or at the landing camp if your faction does not. Completing this quest awards three Stone Keeper's Shards, which is almost like killing a heroic dungeon boss when you have Essence of Wintergrasp. It also gives 13 Gold 23 Silver, and 1241 Honor at Level 80. Because you also gain Honor while killing the requisite 20 players, this is a good quest for Honor grinding.
I highly recommend taking the trip to Icecrown and picking up the dailies Make Them Pay! if you're Horde and No Mercy! if you're Alliance from the floating airships. Kills made in Wintergrasp will count towards these quests, including siege vehicles, which count as a player of the opposing faction. This makes either quest extremely easy to complete while in Wintergrasp. The quests award 13 Gold 23 Silver and 800 bonus Honor at Level 80.
A Rare Herb (A) / Healing With Roses (H)
These quests are part of the elemental farming series that randomly change every day. Alliance players may get the quest from Anchorite Tessa and Horde players from Primalist Mulfort. It requires killing Living Lashers or enemy players in the Steppe of Life in Southwestern Wintergrasp. The drop -- Alliance or Horde Herb Pouches -- comes from the plant elementals as well as opposing players. Players have a higher chance to drop the item and in larger quantities (up to two).
In Patch 3.0.8, players will have a buff indicating what quest item they will drop when killed. This will make farming the drop easier and presumably not limited to the zone. This is an awesome change because it means players can complete these kinds of quests while battling for the Fortress simply by looting slain opponents.
These quests aren't as good to farm through simply killing Living Lashers because of the low drop rate and because there are no greater elemental versions of the plant elementals even if you control Wintergrasp. Completing this quest rewards three Stone Keeper's Shards, 13 Gold 23 Silver, and 1241 Honor at Level 80.
Bones and Arrows (A / H)
This quest may be obtained from Bowyer Randolph if you're Alliance and from Lieutenant Vieron Blazefeather if you're Horde. The required drops, Quiver of Dragonbone Arrows, come from the shadow elementals in the Forest of Shadows in Western Wintergrasp, as well as opposing players. Players and Shadow Revenants have a chance to drop up to two of the quest item, so unlike the previous quests where it makes no difference, it's best to do this when your faction controls the zone. Completing the quest rewards three Stone Keeper's Shards, 13 Gold 23 Silver, and 1241 Honor at Level 80.