Leystone Ore

Legion introduces three new items that you can use to speed up farming ores. These three items are: [Leystone Hoofplates],[Demonsteel Stirrups], [Stonehide Leather Barding]. You should use these if you can find them cheap on the Auction House, or craft it yourself if you can. Every mobs scales to your level in Legion, so it will be a lot harder to avoid the mobs attacking you while you try to farm ores. The combination of these three will make farming ores a lot easier, but the one I would recommend the most is [Demonsteel Stirrups], which let's you mine ores while mounted.
You should also enchant your gloves with [Legion Mining].
Val'SharahThis is the route I use the most because you can avoid most mobs, and there is not that much vertical up and down movement in the zone compared to something like Highmountain.

SuramarSuramar is a level 110 zone, so you can't farm here at lower levels.

AzsunaThere is a bunch Lagoon Basilisks at Azsuna that you can kill and then mine Leystone Ores from their corpses. The respawn rate is fast enough for farming here without downtime.
The downsides are that you won't get any Felstate here, unless you have the shoulder enchant mentioned above, and the place might not work if more than one player tries to farm there.
You can't mine the mobs if someone else is tagging them but refuse to loot it!