Take breaks. Unless you're straight up no-lifing it over a weekend or something, this leveling process is going to take ~40 hours. But any time you do need to step away, log out. That tiny little bit of rested exp is insignificant...but you never know when something might come up and you'll have to leave for a longer period of time than you expected. Better to be logged out and safe(especially with War Mode on) than AFK waiting for a d/c. Plus, you'll need to stretch, eat, shower, and maybe sleep. XD
Once characters reach the level cap, gameplay turns from leveling to the end-game. This represents the culmination of the leveling process and the beginning of the deeper challenges awaiting max-level characters. While play prior to this point is oriented around accumulating experience and gaining new skills, the end-game represents the polished 'final destination' for players, at which characters are fully developed and ready to tackle the biggest challenges in the game, or to relax and make their own adventure.
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