The first time you enter the game after defeating the Pokemon League, you'll be at your house. Move over and talk with your Mum. Cedric Juniper, Professor Juniper's husband will barge in and hand you the National Dex . Sweet! Your Pokedex is now upgraded!
Cedric will leave and you mother will hand you two Max Revives . It's time to leave the house! Outside you'll be stopped by Hugh and his little sister. As well as being thanked, you'll receive a tip about Zoroark at Victory Road. This means you can now visit N's Castle !
Other than that, that's pretty much all there is to do here! Elsewhere in Unova, many additional areas have opened up and there are new events in old places. Feel free to look through the rest of this Post-Game section and do anything that tickles your fancy.
Note that some of the new stuff is probably a bit too difficult for you right now. If you want to play it safe, we advise following the order of events in our guide, at least to a certain degree. So while you might be excited to battle Cynthia for example, you might want to leave her for later.
In addition to what's listed, you can also battle the Elite Four again. However their Pokemon will be higher Level, so you may want to return after some training. Furthermore, you can now encounter Pokemon swarms in the wild. To check what swarms are available, simply check the scrolling sign in any route gatehouse.