What do you after beat the 4th gym leader in blue?

- Go south on Route 8 and defeat the Rocket Grunts at the entrance to Mt. Moon for HM04 Strength

- Enter Mt. Moon, find your rival Blue, and defeat Team Rocket Grunts inside

- Continue to the very center and get HM05 Flash (it is in one of the small side tunnels)

- Get out via the upper left of Mt. Moon, then make your way through Route 9

- At Route 10 go straight ahead into Cerulean City

- Heal Pokémon at the Pokémon Center

- Go West from Pokémon Center into Route 4, where Misty's house/the Cerulean City Gym should be