Sorry, it's late, so this is just a cursory glance at how you'd want to start back...there's a LOT of stuff to go over...but I'd focus on
First, unlock stuff:
(1) complete all the main story quests, which includes most of the hard mode trials
(2) unlock all the new dungeons you've missed:
The Lost City of Amdapor
Halatali (Hard)
Brayflox's Longstop (Hard)
Hullbreaker Isle
The Tam-Tara Deepcroft (Hard)
The Stone Vigil (Hard)
Syrcus Tower (Crystal Tower 2, people call it ST)
anything new in 2.4
(3) do the hildebrand quests at least until you fight gilgamesh
Next, or really concurrently, work on gathering tomes to buy gear with. There used to be Myth tomes (capped at 300 per week, later raised to 450) and Philosophy tomes (unlimited per week); then philosophy went away and we currently have Soldiery (450 / week) and Myth; a week from tomorrow 2.4 is released and we'll have Poetry (or some similar name, capped #/week ) and Soldiery, while myth will be phased out. The higher tier tomes are always used for the newer, higher level purchasable gear. So get as much as you can to buy new gear with!
There's a bunch of other stuff to do, like the new Hunts (think NMs, but they drop allied seals, a currency, rather than gear), but I won't go into the rest now except for maybe a quick rundown of the relic weapon quest line is:
Base relic weapon (ilvl80) > Zenith (90) > Atma (100, kinda) > Animus (100 for real) > Novus (110) > Nexus (115)
You always go to Gerolt in Hrystmill or a new guy also in Hyrstmill to start the next phase of the quest.
For the Atma phase, you have to equip your Zenith weapon and collect an atma from fates in each of 12 different specific zones. Drop rate is incredibly random, and you can get lucky and get them all in 12hrs or it could take an ungodly amount of time if you're unlucky...but 2.4 is supposed to more-than-double the drop rates, yay!
Animus phase is composed of purchasing 9 'books' from an NPC with tomes, 1 at a time. Each book requires you do 3 specific dungeons, 3 fates, 3 leves, and kill 10x 10 open-world enemies (100 total) with your Atma weapon equipped to complete.
Novus phase = purchase a scroll with tomes, and meld 75 total materia to the scroll with 75 alexandrite, for which there are a few different ways to obtain. Alex takes a little time, but materia can take quite a bit of $$. Might want to do some of your own spiritbonding for that.
Nexus phase = equip your Novus and do fates/dungeons/raids ad infinitum, gathering "lights" for each completion. You basically need 2000 lights, and you get 1-16 "lights" depending on the activity you're doing (
nexus light info)