If you like character development and action, then you'll enjoy sword art online.

If you enjoy the worldbuilding and politics, I'd push you towards Log Horizon.

Finally, another series worth considering is Accel World - more of a sci-fi action series than a classic high fantasy ones, but it retains similar elements to Danmachi (which is the anime you were talking about). It's by the same author as SAO, but done in a very different style and aesthetic.

I can also point you to a bunch of webnovels and books in this genre, if you're hungry for more. That's more or less all I've got for anime, though.



Edited 1 time(s). Last edit at 08/03/2015 10:30AM by vortexmagus.