A good place to start fishing is on magikarp in Vermilion City then on horsea and krabby at level 5.
All pokemon in Viridian City, Route 22 and Viridian Forest Clearing though are level 1 or 0 fishing so they are even better places to start.
Route 24 just above Cerulean City should also have karps at level 1 fishing so I assume you're trying to fish outside Cerulean Cave with higher level pokemon and therefore fishing levels.
The guide below is for Kanto fishing levels, Johto has yet to be updated and information on those levels can be found on the Fishing page of the PWO wiki.
Fishing level Zero - Magikarp under level 15. Golden in Viridian Forest Clearing.
Fishing level 1 - All pokémon under lvl 10 bar the exceptions.
Fishing level 5 - All pokémon under lvl 20 bar the exceptions.
Fishing level 10 - All pokémon under lvl 30 bar the exceptions.
Fishing level 20 - All pokémon under lvl 40 bar the exceptions.
Fishing level 30 - All pokémon over lvl 40 bar the exceptions.
Fishing level 30 - Shellder (Any Level)
Fishing level 40 - dratini (Any level)
Add 5 fishing levels for higher evolutions, for example level 25 Seaking would need level 15 fishing skill.