MSQ, job quests and "blue icon" quests are your priorities. If you skipped to story Lv50 then a lot of the dungeon-unlock sidequests will have been cleared already for you, but any remaining quests with blue icons will be important to some extent.

For gameplay purposes, have you:
- unlocked the challenge log? (sidequest from the Drowning Wench tavern in Limsa)
- got your chocobo as a battle partner? (Camp Tranquil in South Shroud)

For story, make sure you do the optional Lv50 Crystal Tower raids starting near the aetheryte plaza at Revenant's Toll, as this ties into Shadowbringers' plot. The Warring Triad and Alexander raids at Lv60 and Omega at Lv70 are worthwhile too.

Don't rush to Lv80 just for the sake of being Lv80 though. You won't unlock anything until you reach certain points in the MSQ - specifically completing Shadowbringers to have any access to endgame content.