If your goal is to catch up to 57~60 quickly so that you can continue the story on SAM, one of the popular options is to level in Palace of the Dead (Lv17 quest in Gridania Adventurers' Guild, "The House That Death Built"). Once you clear floors 1-50 (a fairly easy feat), you can begin fresh runs at floor 51. Between Lv50 and LV60, you'll gain a level per 3 to 5 runs (3/Lv for low 50s, 5/Lv for high 50s). One run is 10 floors, 51-60, 61-70, etc; you can continue going deeper, or restart and do 51-60 over and over.

This is probably your fastest option outside of making friends with a tank/healer who can run level-appropriate dungeons with you.