Congratulations!! It will go by fast if you do the following:
1. Spend only no more than 90 minutes max on MSQ, mostly are fetch quests + talk to npc + check things out. But doing them in long stretch will make you want to hate this game. You should be able to clear them in about a week or ten days doing this. Each patches is about 5 hours long or less. Up to you if you want to burn five hours a day to clear each patch though.
2. Unlock the other 15 dungeons. You should mix this up, clear 2-3 dungeons if possible a day, grab any friends or FC members along with you for the first time bonus.
3. Ilevel bump tips: ask any of your FC members or friends, who have access to Ishgard, to buy you normal quality accessories level 115 ASAP now from vendor in Ishgard stores. Yes you will get level 110 weapon, gears, and accessories down the road on MSQ, but you still have to clear those dungeons, etc, by getting normal quality stuffs earlier, it makes doing them so much easier. Do not pay inflated price in the market board, but do check the gears + accessories, sometimes undercutter may put things below vendor prices.
4. To avoid massive burn out, mix it up with doing daily roulette stuffs, leveling other lower level jobs that you may overlook for your cross class. And doing your crafting and gathering. Plus the usual weekly challenge on FATE, levequest, etc...
5. You will have to do those Hard Mode original three primal for main story quest, yes they will not let you get away from this, so may as well unlock your Relic Weapon quests, and get them all done for level 90 glamour weapon :)
6. Make sure you max up your grand company standing and able to unlock Hunt Board. You will use this feature more in 3.0. so get that done if you have not done it yet.
