Pokeatlon Dome is place where you can compete in competitions. You compete with your Pokemon and control them with stylus. In every competion you win points and you'll be able to buy some stuff with them from the Pokeathlon Shop that's also inside the building (including potions, rare candy, evolution stones) The prizes that you can buy change daily, so you'll need to check back every day if you are looking for a specific item.
The PokeAthlon Dome is west of the National Park above Goldenrod City. When going north from Goldenrod, enter the building just before the National Park. Head to the left and up the other door (the one that doesn't lead to the park) and you will find the PokeAthlon Dome.
buy it with 2550 points in the athlete shop in the pokéathlon dome.
You can only buy each item once per day.
I'm not sure where you can find it, but I know that on one day you can buy it for 2500 Athlete Points at the Pokeathlon Dome.
After two days competing in the pokeathlon in the poke dome it was available to me for 1000 points
The Pokeathlon Dome did not exist prior to Heartgold/Soulsilver, so it wasn't in Crystal.
You can buy a sunstone from the pokeathlon shop inside of the pokeathlon dome
Go to the national park and from there you should be able to the pokeathlon dome in poke mon heart gold.
at the pokeathlon dome on Thursday
On Pokemon Soul Silver and Pokemon Heart Gold, you have to defeat the Goldenrod City Gym Leader, Whitney, and then she tells you that the construction for the Pokeathlon Dome is complete.
as a prize in the pokeathlon dome on certain days
At the pokeathlon dome as a prize on Wednesday.
you jump 1000 times
The Pokeathlon Dome is only in Heartgold and Soulsilver. But, there are contests in Platinum. Just go to Hearthome City and go to the northernmost part of the city to reach the contest hall.
Travel north of Goldenrod City between routes 35 and 36. The Pokeathlon is connected to the National Park.
you can earn it in the pokeathlon dome on specific days
no get them at the pokeathlon dome