For the gym:
You are supposed to get past the psyducks in Solaceon by following a galactic grunt in pastoria then getting a special item from Cynthia then give it to the psyducks and deliver a charm for Cynthia. Then Fantina will arrive at the gym in hearthome. Hope this helps!
you beat the gym leader
In both diamond and pearl the one city is Hearthome
Hearthome city
Hearthome city isnt in that game. Hearthome city is in Diamond, Pearl, and Platinum.
south of hearthome city
Between pastoria city and hearthome city.
in hearthome city
In the northern part of Hearthome city
if you mean how to get there its in hearthome city
east of hearthome city
You can get one in hearthome city.
go down to the road under hearthome city.