sunyshore city, but first you need to go to the peak of mt coronet and catch palkia because the man near sunyshore will tell you there was a blackout and wont let you past unless you have palkia.
P-S, you cant just trade a palkia from another game, you need to do the event where cyrus and the rest of team galactic are there trying to use palkia. so catch palkia yourself!!
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You can't you just have to beat him and get it
Hearthome's badge
Get the first gym badge
You can use the GTS in Pokemon Platinum after you get the first gym badge from the Oreburgh City gym.
Once you obtain a badge it's permanently stored in the badge case.