E
Embree
I've recently beaten the Elite 4 for the first time (thus ending the main storyline), and like some of the previous generations, the league's pokemon got much harder. Therefor, I'm not sure where to train.
Grind with Audinos; they give a ton of EXP for beating them. Or go to the Giant Hole, where Pokemon are levels 55-60.
i had this problem, as well. what i decided to do was choose the grass in the new routes that open up after the game has ended. the levels vary, so it was pretty good helping get through the 40's & some of the 50's, and even exp. sharing weaker pokemon from the 30's.
I trained in the Nimbasa city stadiums, there are a lot of trainers and they give a huge amount of EXP. Just to demonstrate how good it is, I'll often go there for grinding my pokemon to level 50 after EV training.
New Routes, Victory Road, or Nimbasa City Stadiums. Giant Hole you can't get to without battling trainers...but the trainers have weak Pokemon anyway.
Go to the eastern cities, they have decent level trainers there, or if you have the black city go there.
I went to the east, defeating every single trainer I met, and ofcourse trained in Nimbasa every day, and batteling Cheren can help too.
Final room in Victory Road.
You can train with Cynthia,Morimoto,at the Nimbasa Domes,Triple Battles on Opelucid City EVERYDAY,Saturdays with Bianca,all the trainers from the Routes 11,12,13,14,15 and 16,with the wild Pokemon of the Great Chasm,with Cheren,the Royal Unova...And finally,at the Elite 4 
How do I get into giant chasm. I'm on route 13 but can't find the enterance.
You need to go to the sea, go as far north as you can next to the old man, use surf and go around the rocks. You come back to where you were orginally but behind the strength bolder. Go forward and you'll soon find yourself by a cave, go inside and viola.
