What do you mean by "post-game"? You mean after beating the Pokemon League? There's lost of stuff to do after that, and it all depends on the game you're playing! You could always:
- Try to complete the Pokedex, or catch and evolve as many Pokemon as you can!
- Create an ultimate team, that can beat just about anybody;
- Discover hidden secrets in the game. If you're playing FR/LG, there's a lot of secrets in the seven islands, especially after the League (The Team Rocket quest, catching Mewtwo).
The game isn't over with the Pokemon League. Just look around in the Pokemon world a bit, and you'll find something to do.