After defeating Brock, head east from Pewter City onto Route 3, then through Mt. Moon, a cave filled with Zubat and Geodude. Mt. Moon is also where you'll encounter Team Rocket for the first time. Exit Mt. Moon to reach Route 4 and then Cerulean City. Here, you'll face Misty, the Water-type Gym Leader. After earning your second badge, you'll need to deal with Team Rocket again before heading south towards Vermilion City.
