Before heading straight to all the new fangled postgame locations, spare a thought for some of the old places that you haven't visited in absolute ages. While you won't find much new there, perhaps you'll find some items or easter eggs you missed earlier.
As for what's definitely new, head back to Professor Juniper's lab in Nuvema Town . You can find Bianca here, offering you advice to ensure your postgame adventure is eventful. On Saturday Nights, you can even challenge her to a Pokemon battle!
Trainer Battle: Bianca
|Simipour||63||Water||Only if you picked Tepig|
|Simisage||63||Grass||Only if you picked Oshawott|
|Simisear||63||Fire||Only if you picked Snivy|
|Serperior||65||Grass||Only if you picked Tepig|
|Emboar||65||Fire||Only if you picked Oshawott|
|Samurott||65||Water||Only if you picked Snivy|
Basically her original team with added Mienshao and Chandelure. You already fought both of these Pokemon during your Elite Four campaign, so they shouldn't surprise you.
After showing Bianca who's boss, set a course for Nimbasa City and head into Route 5. South of the trailer, you can find Cheren mulling over his Pokemon career. In the end, he leaves, but not before inviting you for a rematch. Now you can battle Cheren at the end of Victory Road daily.
Trainer Battle: Cheren
|Simisear||65||Water||Only if you picked Tepig|
|Simipour||65||Grass||Only if you picked Oshawott|
|Simisage||65||Fire||Only if you picked Snivy|
|Samurott||67||Water||Only if you picked Tepig|
|Serperior||67||Grass||Only if you picked Oshawott|
|Emboar||67||Fire/Fighting||Only if you picked Snivy|
Like Bianca, Cheren uses his regular party, plus Gigalith and Haxorus. Haxorus, you'll know is pretty beastly from your final Gym battle. Gigalith is pretty tough too, with a combination of Sturdy (cannot be OHKO) and Stone Edge (high critical) causing potential fatalities.
Upon emerging victorious for the 8th or so time, there's one more battle to mention, but one that you may want to delay until later. When your Pokemon are suitably strong enough, return to the GAME FREAK HQ in Castelia City and speak to the man in the group of three on the right...
Trainer Battle: GAME FREAK Morimoto
Morimoto is a programmer at GAME FREAK, so you're kind of fighting a god here. Luckily, his Pokemon aren't immensely powerful, disregarding their high Levels. At least you're not fighting Arceus and five other Legendary Pokemon!