PokéBase - Pokémon Q&A
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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