You can go to Snowpoint city and ride the boat to the Fight area. You can play the Battle tower and fight your Rival on weekends. If you finish your pokedex, you can go to the Resort area and the Survival Area. In the Stark Mountain, you can catch Heatran, An area opens up on route 214 and you can go catch Giratina.
Source - http://www.gamefaqs.com/ds/925601-pokemon-diamond-version/answers/3101-any-suggestions-on-what-to-do-after-beating-the-game
^Diamond & Pearl are the same Post-Game
