How to farm honor without battlegrounds or PvP (World of Warcraft: Legion)

It is possible to farm honor without ever participating in PvP activities in Legion, and this is done in the north-west corner of Azsuna. Here you will find King Mrgl-Mrgl which has a quest that requires you to gather Timeworn Artifacts. These items drop from any mob in the surrounding area, and the first quest requires you to get only one of these items, and turn them in for 200 honor. After this, you can keep collecting more Timeworn Artifacts, and each one provides you with 1 honor.

Getting the Timeworn Artifacts

The artifacts drop from any enemy in the area around King Mrgl-Mrgl, and one enemy drops around 3 artifacts. There are only Timeworn Jars in the area, and each of these containers have 17-20 artifacts within them, so make sure to pick these up as well.
You can loot up to 1000 artifacts before you have to turn them in, but note that this is a free-for-all PvP area, so you can be killed by anyone, and you drop all your artifacts upon death! So it's best to farm them when there are few people around, and turn them in often.

Getting honor this way is about the same pace as playing in regular battleground, but by farming this at off-peak hours, you can gain PvP levels without ever participating in PvP.