You can take on the Elite Four again, they will be higher level than before.
Once you have defeated all 16 gyms you can go to Mt. Silver and take on Red. His pokemon are level 80-88 so be prepared.
After defeated Red go and talk to some of the key people in the game like Professor Oak, Mr. Pokemon, they will have surprises for you.
There are also a ton of legendaries in the games, like ohioscyther said. See this question: http://pokemondb.net/pokebase/763/what-are-all-rare-pokemon-you-catch-heartgold-and-soulsilver