Old Rod:
RBY: Vermillion City (Fishing Guru)
GSC: (Johto) Route 32 (Man inside Pokemon Center)
RSE: Dewford Town (Fisherman)
DP/Pt: Jubilife City (Fishing Guru)
HGSS: (Johto) Route 32 (Fishing Guru)
XY: Ambrette Town
ORAS: Dewford Town
Good Rod:
RBY: Fuchsia City (Fishing Guru)
GSC: (Johto) Olivine City (Sailor - House by the Pokemart)
RSE: Route 118 (Fisherman)
DP/Pt: Hearthome City (Fishing Guru)
HGSS: (Johto) Olivine City (Fishing Guru)
XY: Coumarine City
ORAS: Route 118
Super Rod:
RBY: Route 12 (Fishing Guru)
GSC: (Kanto) Route 12 (Fisherman in the house)
RSE: Mossdeep City (Fisherman)
FRLG: Route 12 (Fishing Guru's younger brother)
DP/Pt: Fight Area (Fishing Guru)
HGSS: (Kanto) Route 12 (Fishing Guru)
BW/B2W2: Nuvema Town (Gift from Looker (BW) or Cedric (B2W2))
XY: Route 16
ORAS: Mossdeep City
In Sun/Moon, it appears that there is only one fishing rod found at Akala Island, Brooklet Hill (source)
Sources for Gens 1-6:
https://www.serebii.net/itemdex/oldrod.shtml
https://www.serebii.net/itemdex/goodrod.shtml
https://www.serebii.net/itemdex/superrod.shtml
