If you want to spend as little time on your alt as possible - just do Legion Invasions. You can use sites like (https://wow.gameinfo.io/invasions) to track when the next invasion will be. Log in, fly to the closest world quest, and once there - right-click on the quest's name in your quest log and "Find Group". Sign up for some group, or if there's none - just start your own immediately, and people will come to you. It is 10 times faster to do invasion quests in a group. Once that particular quest is complete - leave the group, and fly to the next one, where you should find another group. Don't expect the group from one world quest to follow you to the next. Then you simply log out until next invasion. You can do 1-2 invasions a day, and each invasion will give you about a level or 1.5 of experience, if you have full heirloom gear. Each invasion will take about 20 minutes.
After completing your island expedition and second foothold, head back out to your third and final zone to quest in. Note that any legendaries you were using to level have become inactive and are merely stat sticks now. Feel free to replace them with quest gear as you obtain it. Before heading out, feel free to send your three champions out on new missions!
Drustvar is far and away the hardest Alliance zone, which is exactly why you want to do it first. If you have legendary items, they’ll still be usable, and if you don’t, this zone will still be easier early on than it will be later. Drustvar is also extremely fast and will let you jump out ahead of your competition in other zones, which means fewer players around to take your quest objectives.
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While Leveling your characters in BfA you'll also need to complete the new War Campaign quests in order to unlock world quests and the ability to venture to the other factions contintent. We cover all of this in our War Campaign guides and with out new Guide Tabs feature you can have both Leveling and War Campaign guides loaded at the same time to easily switch between them.
The dark side of this disparity is griefing; max level players are able to easily disrupt questing areas in use by players of the opposite faction, and can one-shot most enemy characters. Sadly, even guards in most areas are unable to stand against well-equipped max level players, especially as the current expansion progresses and gear steadily increases in power. Of course, the best answer to this is usually to recruit some max level players of your own faction, or switch to a max level alt, and make the griefer regret the day they flew into Goldshire.
Congratulations on reaching Level 120! There are a myriad of new things to do. The first thing you should do is head to your faction hub ship where you have been doing your mission table quests and footholds to pick up and complete the quests necessary to unlock World Quests. World Quests will provide you an opportunity to grind reputation levels, acquire gear, and gather Azerite. There are tons of new things to do that we will cover in our Level 120 Battle Guide found here: Level 120 Battle Guide