The last 11 days before Heavensward. If you aren't sure what to do in these remaining days, here are some ideas.
Finish Main Story Quests This is required to do Heavensward content and should be your highest priority. Finish these quests before early access starts. You can't even level the new classes without having this finished.
Max Rested XP - 10 days - Start by 2am PST Tuesday June 9th. This will give a free 1.5 levels towards your first levelled class once Heavensward hits. To accumulate, be sure not to play any class that is not level 50 after the above date and time.
Max Leves - 16.5 days - Start already (if you’re completely out) Max leve is 99, and accumulation rate is 3 per 12 hours. These will be important for levelling as well, although I do not encourage you to leve your way to 60 on your primary combat class - do the quests! Leves are better suited for secondary combat class or DoH/DoL levelling.
Gear Up Main Class(es) Make sure you have a reasonable set of gear on your main classes. The ilvl is expected to increase quite quickly after release, so the current absolute top end gear isn’t necessary. Aim for at least ilvl 100.
Cleared Out Inventory Clear out your inventory. Clear out your retainers’ inventories. Remove things that you will likely never use even if you have some attachment to them. You want to deal with inventory as little as possible going into new content, and you certainly don’t want to get confused on what is new and what isn’t. I’m going to fully empty one of my retainers and use that one solely for heavensward stuff.
Cleared Quest Log Yeah, those old level 46 quests you’ve had in your log for the past 3 months? Now’s the time to drop them. You’re never going to do them. You may even want to drop unfinished content quests (Ramuh Ex quest, etc) just to have a fully clear log. Up to you.
Food Items Make sure you have a reasonable supply of food for the first 2-3 classes you expect to level. Don’t go too crazy - there will of course be new food to buy after the first few weeks.
Gil While never an absolute necessity in FFXIV, gil tends to help speed things up significantly. You can buy pieces of gear that you need to round out your set, and you can avoid farming for things that might be sellable on the MB. The more the merrier, but if you want enough to handle everything from housing to endgame.
Max GC Seals Should be easy to do running 50 dungeons and greeding gear. There will be new GC ranks.It’s not confirmed, but most people seem to expect them to keep the same GC currency for the new ranks.
Ventures Retainers will be able to level towards 60 with you, so be sure to stock up on some ventures so you don’t have to farm them.
Cross Classes Levelled If you’re going to roll one of the new classes, make sure you have the appropriate cross classes levelled up (usually to 34).DRK = Gladiator/Maurader AST = Conjurer/Thaumaturge MCH = Archer/Lancer
Glamour Your Winter Gear You can’t be wearing your summer hats to Coerthas, can you? Find some nice thick wool or furred gear and get yourself glamoured. Keep it sexy.
Gear for New Class Levelling up one of the new classes? Have a full set of gear (or two) ready for them. They will start at level 30, so some folks are going as hardcore as having a full set of level 30, 35, 40, 45, and 50 gear ready for them. Probably don’t need to be that prepared.
Max Allied Seals No one knows if these are going to continue. There may be a new hunt currency entirely. Even so, couldn’t hurt to have some reasonable amount of these farmed and ready.
UI Issues If you’ve been putting off minor fixes to your UI, now’s the time to do it. DPS and don’t quickly notice when you proc something? Move that closer to center screen. Need to setup a hotbar common to all classes but haven’t gotten around to it? Do it now.if you need to re-organize your hotbars to have free slots for the new abilities, do it now! You will have to learn a new rotation, so it's a good time to optimize your button presses.
Max Finished Leves Some people are finishing the max leves before the expansion hits and keeping those leves in their journal rather than turning them in. This will allow them to immediately turn in all 16 leves when the level cap is raised to gain some quick xp. I don’t think this will boost you much, and there will be a lot of new quests which will be more efficient. Probably not that important. EDIT: Remember you can only turn leves in for the class you did them on, so this won't work for the new classes. You can also prep any remaining non-leve quests for turn-in rather than abandoning them to free up log space!
Finish Hunting Log Make sure all your primary classes have a hunting log completed to level 50. This will likely be required to unlock the 50-60 log entries.
Poetics Weapon For New Class Tip-- If you have time, get your poetics tokens and other mats for an ilvl 130 ironworks weapon for whatever new class you intend to play. There is evidence the new classes will be getting ironworks weapons.