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Soaring - go to different Mirage Islands to get Pokemon not native to Hoenn. You can also find legendaries from other games if you fulfill certain requirements
Secret Bases - build your own, battle other people in theirs, and bring them to your own as a Secret Pal (you may want to look into Blissey bases, it's an incredibly easy way to train your team for when you get to...)
Train for competition - this is the first game I've ever bothered with things like EV trainings and team synergy. Granted, it's way easier in this game than it was in previous games, so it's not as intimidating once you read a few guides and practice a bit. There's satisfaction in creating the perfect Pokemon. It's also a good way to use Pokemon you wouldn't normally use. One of my friends gave me three random Pokemon that I was supposed to train for competition, and I ended up loving them to pieces.
