Dewford Town is a small town located in an island in the middle of Route 106 and Route 107. One of the most notable building here is the Dewford (Town) Hall where you can influence the people's idea of a current "trend" by talking to the boy outside the hall. Disagree with him and he'll ask you to specify what is "in". From there, you can select an item and a corresponding word that makes the item popular.
After getting the Balance Badge, you can return in the Hall and find a man with glasses to receive a TM36 Sludge Bomb.
Talk to the fisherman to the east of Dewform Gym to get an Old Rod. To the north, you'll find two houses. Enter the one on the right and talk to the man sitting in front of the table to get a Silk Scarf.
After checking out those points of interest, prepare your best anti-Fighting type party and head to the Gym.