Forgettable encounter areas
Fishing/Surfing in the Towns/Cities.
South and North of Cycling Road.
Lapras in Silph Co.
Fossil in Cinnabar Island Lab; debatable as to whether it's a different area than Cinnabar Island proper.
East of Saffron City, requires Cut.
Eevee or Celadon Game Corner rewards.
Grass Patch below Pallet Town.
Treasure Beach (Below the port on Archi 7's first Island)
Make sure to visit the route to the west of Viridian City early on, and make sure to not advance past the first patch of grass if you don't want to fight your rival.
Always carry something to cure the poison status, if possible. When in Viridian forest, beware of Weedles.
Remember you can't evolve pokemon that aren't part of the original 151 ones, so forget about Kingdra or Steelix.
It's recommended to play with a dupes clause if you don't mind fighting a few Pokemon until you find one that you don't have, as Pokemon tend to repeat a lot. If you don't have the time or patience to do it, ignore the dupes clause.