The earliest in the game you can get to Vermillion City is once you have reached Cerulean City. Once in Cerulean City, go north. There, travel north then east while battlling your Rival and other trainers on the way. Once you have reach Bill's House, talk to Bill and help him out. Then come back down to Cerulean City and go into the house on the Northeast side with a Police outside. Go out the back hole and fight a Rocket. Once you win, you can then travel around Cerulean City and go south to where you will find an underground passage. Go through the underground passage to reach Vermillion City.
Vermilion city
Southern Vermilion City
It's south of Vermilion city.
after you deliver oaks' parcel then you go to vermilion city in the Pokemon center
The Pokemon Fan Club is located at the Northwestern part of Vermilion City.
The ship SS Anne will never return in yellow version.
The third Gym Leader is Lt. Surge and you can find him in Vermilion City.
North of Vermilion city is lake surf on it and eventualy you will encounter Psyduck.
TM24 is given by Lt Surge after his defeat at the Vermilion City gym.
You talk to Officer Jenny in Vermilion City after getting the Thunder Badge, then she'll give it to you.
Officer Jenny can be found in Vermilion City and will give you a Squirtle once you've proved yourself.
Officer Jenny is in Vermilion City. She gives you a Squirtle after you defeat Lt. Surge if you have the starter Pikachu in your team.