The quest to unlock the Crystal Tower raids starts in Saint Coinach's, Mor Dhona. These two raids will net you everything you need to be geared up for anything but the hardest end game. As a healer, one run including queue times should take about an hour of your time. (Queue time depends on time of day and day of week of course.) It's technically the best use of your time, but won't net you a lot of income, and will get repetitive really fast.

For the sake of variety, also unlock at least all available dungeons (some of them unlock through the main storyline, others are unlocked from various places all over the map, check your map for lvl 50 quest icons) and run daily roulette for extra tomes and lots of gil. One dungeon run commonly takes around 30 minutes for healers, but may go up to 60 if the group is new or disorganised (or someone needs to go AFK). Unlocking all storyline primals and their hard modes if applicable and the Hildibrand questline will also give you Trial roulette, which is potentially the fastest (an overgeared group can finish a primal fight in ten minutes), but also has a higher chance of repeat wipes (some players have no patience for properly doing mechanics in roulette).