My Horde warrior is up to over 18,000 honor points, and has over 30 marks of honor from each battleground. So which of these battlegrounds is the best place to farm honor? In my opinion Arathi Basin is the place to go. The reason for that is that in AB it doesn't matter much whether you win or lose. You get bonus honor based on the resources your side gathered. So if you lose, but have lets say 1,650 resources to the winner's 2,000, you still get 100 bonus honor to the victor's 120 bonus honor. Not much of a difference. Add to this the fact that it is nearly impossible to totally stall a Arathi Basin game, and you have a honor point farming winner.
Second best for honor is Alterac Valley. In the shorter AV battles both sides make as much honor as in Arathi Basin. On the AV bonus honor weekends probably even more. The problem is that in AV you only get good honor in the first half hour or so. After that most of the named NPCs that give 14 points of honor are dead, and for killing players of the other faction the diminished returns rule applies, giving less and less honor the more often the same guy gets killed. When an enemy player is worth only 1 honor point, regardless of rank, and there is no more bonus honor to gain, grinding AV for honor is not a good idea. When I join an Alterac Valley battle and find I've just joined a combat which has been going on already for over 1 hour, I just /afk out. The 15 minutes deserter buff is a less harsh penalty than staying in a long AV battle.
The worst place for honor is Warsong Gulch. This is due to the high number of premade groups in that battleground. If you are member of a pickup group and the other side has a premade group, it is quite possible not to capture a single flag, and thus get no bonus honor at all. Even if you are member of a premade group and get paired against another premade group, the honor yield isn't great, because two premade groups often stall each other and draw out the battle. That can be fun, but it isn't great from a honor grind perspective.
Following the wise advice from a reader, I also tried the battlegrounds with my Alliance priest, thus getting the other point of view. For WSG and AB that doesn't make much of a difference. In AV I did three battles, all three of which the Alliance won in 25 minutes or less, which obviously was good honor gain. But in the end farming Alterac Valley for honor as Alliance didn't give much more honor than doing it as Horde. Because as Horde I can join any battleground in under 1 minute, while as Alliance the AV queues I experienced were 10 to 12 minutes long, adding over half an hour of no honor gain at all to the total time spent in the three battles.
So to summarize "Tobold's Guide to Honor Farming", my recommendation would be to alternate AB and AV, and just doing enough WSG to have the marks of honor you need. Doing just Arathi Basin gives slightly better honor, but is getting repetitive real fast. Doing Alterac Valley as well is more variety, more fun, and nearly the same amount of honor. Stay away from Warsong Gulch, unless you have a premade group, and even then it isn't the perfect place to farm honor.