The current objective is telling me to explore Hearthome city. This was after I met the gym leader at the contest hall. I have gone into the buildings and have spoken with the townspeople and the objective has not updated, it is still asking me to explore the town. What am I supposed to be looking for here?
You have to exit the town the way you came and you will meet your usual buddy who will. Challenge you to a fight. Defeat him and you will get an updated objective to go to a different city and fight a gym leader there.