after defeating the johto Pokemon league u catch the ferry at olivine.this takes u to vermillion city :)
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the doll is in vermillion city in the Pokemon fan club
In the fan club in Vermillion City.
There are two entrances to Diglett Cave. One is East of Vermillion City, the other South of Pewter City. -Pokemon Guru
after you have beaten the elite 4 in johto you will get an SS. Aqua ticket which will take you from olivine city to vermillion on Mondays and Fridays. When you're in vermillion you could beat the gm there and in saffron city you don't have to, so just head north until you each cerulean city.
You Find it in the Vermillion City Pokemon Club. and Then once you have it just go up to her and press A