Old Rod: From a fisherman NPC inside the Pokémon Center on Route 32, directly south from Violet City. Travel south down the route all the way and you'll find the Pokecenter just before the entrance to Union Cave.
(Source: Guide Strats)
Good Rod: From a fisherman NPC inside his house in Olivine City. The exact house is pictured below.
(Source: Guide Strats)
Super Rod: From the fisherman NPC inside his house on Route 12 in Kanto, which is located along Silence Bridge. Just travel south from Lavender Town and you'll eventually reach his house, pictured below.
(Source: Guide Strats)