Do after the Delta Episode

This is what you can do in the post-game:

Post Elite-Four

• Collect Starters from 3 different regions from Birch. (Exit your house, and he'll call for help. You can do this 3 times and get starters from each of these regions in this order: Johto, Unova, Sinnoh)

• Collect an Egg from the Old Woman near the hot springs in Lavaridge Town that will hatch into Togepi

• Use Mirage Spots to capture legendaries (see this page for more details where to find them)

• Battle Resort is open, Move Tutor is available, Battle Maison is open

  • Once you have beat a Battle Chatelaine in the Battle Maison, you will be able to rematch Wally once a day

• Complete Hoenn Dex and get Oval Charm

• Complete National Dex and get Shiny Charm

Post Delta Episode

• Collect 1 Beldum from Steven's house in Mossdeep City

• Collect 1 Sharpedo and 1 Camerupt from 2 grunts inside the Battle Resort

• Collect the remaining Megastones. Here's where to find each one:

  • Audinite - Battle Resort (Talk to Looker at the Battle Resort)
  • Blastoisinite - S.S. Tidal - Find it on the ground.
  • Cameruptite - Team Magma's Hideout [Ruby] / Battle Resort [Sapphire] (Get it during the Delta Episode [Ruby] or get it from a Team Magma Grunt at the Battle Resort [Sapphire]).
  • Galladite - Fallarbor Town - Talk to Professor Cozmo in his lab.
  • Gengarite - Battle Resort - Find it on the ground.
  • Latiasite - Litteroot Town [Ruby] - Talk to your Mom in your house.
  • Latiosite - Litteroot Town [Sapphire] - Talk to your Mom in your house.
  • Metagrossite - Pokemon League - Defeat Steven once again after the Delta Episode.
  • Salamencite - Meteor Falls - Talk to the old woman there after the Delta Episode.
  • Sharpendonite - Battle Resort [Ruby] / Team Aqua's Hideout [Sapphire] (Get it from a Team Aqua Grunt at the Battle Resort [Ruby] or get it during the Delta Episode [Sapphire])

Source Reddit.