Diglett's Cave
From Bulbapedia, the community-driven Pokémon encyclopedia.
Diglett's Cave is a burrow that was dug by wild by wild Diglett and Dugtrio. Both of which can be found in abundance inside.
It is famous for connecting Route 2 and Route 11, near Vermilion City. After the main character enters Cerulean City, the only way to return to Pewter City and Viridian City without using Surf or Fly is to travel through Diglett's Cave,