After getting those 3 Grams (Letters) for Wingull on Route 13, he will fly away leaving U-Turn in his place.
Challenger's Cave B2F, east of Protein
Route 6: North of the southernmost bridge (requires Surf)
Route 13: On a cliff in the southwestern corner of the route (requires Strength)
Icirrus City: From an old lady in the Pokémon center's lobby