Where can I train my Pokemon in HeartGold/SoulSilver after Kanto?
I have been using the Elite Four to train my Pokemon while running through Kanto. Unfortunately, I made the mistake of defeating Blue in Viridian City without leveling up my Pokemon enough, so now the upgraded version of the Elite Four is very difficult (All their Pokemon are lvl 60-70). Where is a good place to train in order to quickly level up my Pokemon, which are around the mid to low 50s?
If you have a Sinnoh game from the 4th generation, the best method is actually to trade them to that game and train them up on the wild pokemon in the Battle Zone (the island containing the battle frontier), especially Route 227 and Stark Mountain.
The highest level wild Pokemon in the Johto remakes are the level 45-50 Pokemon in Mt. Silver and the lowest floor or Cerulean Cave.
If you don't have any Sinnoh games, your best option is to keep doing rematches with trainers, which can be found by the exclamation marks next to route names on your Pokegear map (some of those trainers just want to give you items, but most are rematches). or just keep attempting the Elite Four, even if you don't succeed (though this may drastically lower your Pokemon's happiness because of the repeated fainting).
Another option is to do Gym Leader rematches in the Fighting Dojo in Saffron City, but this is slow because you can only fight certain Gym Leaders each day, and you need to collect their phone numbers beforehand. A guide to getting the Gym Leader's phone numbers is available on Bulbapedia.After you get their phone number, call them at the correct time, and they will show up in the Fighting Dojo.
Their Pokemon are levelled up significantly. Most of the Gym leaders are in the 50-60 range, but some (Blue) go up to level 70.
By "battle area", if you mean the battle tower/factory/castle etc. then you don't gain experience there at all. If you mean something else, perhaps you should make it clearer. The rest of this answer is very useful.
@StrixVaria: The island the Battle Frontier is on is called the Battle Area. It contains high levelled wild pokemon.