I forgot to look into the selection of dailies for world PvP. Here’s what I’ve found so far: (note: all are Alliance quests; I assume there are Horde equivalents)
Terokkar Forest
Exorcist Sullivan in Allerian Stronghold (on the edge near the Bone Wastes) gives a quest to help take a tower in the Bone Wastes. Reward is 12g and 209 honor.
Nagrand
Lakoor in Telaar (in the SE of town, look for the blue !) gives a quest to defeat 10 enemy players in Halaa. Reward is 12g and 209 honor.
Are these dailies or just repeatable quests? I heard that the one for 1 mark from each BG is repeatable (maybe only once daily) but the monetary reward is only the first time and is honor only after that. That makes me wonder if these will be the same.
On the PTR, they’re currently listed as “dailies” in the quest log, which means I assume the monetary reward will be constant (as it is with other dailies).
The quest for one-mark-from-each-BG is indeed just a repeatable quest, not a daily, and awards cash+honor for the first handin and only honor thereafter.