>>154478171: Getting Grand Duke/Duchess at the Battle Chateau allows you to get Diantha as an opponent as well as letting you get the Black Write of Challenge which ups everyone's levels in there by 20. Diantha has level 20 stuff by default. Most of the teams of 2-3 Audinos that appear in there become levels 45-65
2: Resturant Le Wow in Lumiose has level 60-65 stuff in double/triple/rotation battles. Costs 100k to get in but you get ~35k back in battles without an amulet coin and up to 156k back for a perfect challenge run so you'll almost always bank a profit
3: Battle your Rival once a day in Kiloude
