Lavender Town is... well, apart from being a lavender colored town... a super-sized cemetery city for Pokémon.
Pokémon nicknames
Ever wanted to go back and change one of your Pokémon's nicknames? Well, here's the only place where you can do it. Enter the building close to the south entrance and talk to the Pokémon "name rater" inside. He will only let you change names of Pokémon you captured yourself.
Once a Pokémon is traded, the name sticks – so be sure to give the Pokémon you're planning to trade with a friend some especially ridiculous names.
Mr. Fuji's house
There isn't much you can do when you first walk into this house. You'll be told that Mr. Fuji is missing, but that's about it.
Pokémon Tower
Don't enter Pokémon Tower just yet. You don't have the necessary tools to engage wild Ghost Pokémon yet, so you can't finish the job. Return here as soon as you've found the Silph Scope – and start training a Psychic Pokémon to be ready for the enemy. The Silph Scope can be found in Celadon City, which can be reached via Routes 8 and 7.
Exit to the left of the screen to go to Route 8.