Back at launch you basically had to FATE grind to finish off the 40s.

Things are much better now. Do a daily low level roulette, guildhest roulette, go after weekly Challenge Log goals (unlock the Challenge Log from a quest in Limsa if you haven't already), do FATES and Leves while you're waiting in queue for dungeons.
Quests alone are not enough for the higher levels but there are plenty of options if you look around.

If you find leveling too grindy at this point even with all of these options you probably won't enjoy the end of the 2.0 story. The main scenario jumps from level 46 to 49 at one point.