Pokémon Red and Blue/Route 1

'Resume your journey north to Viridian City. You can't capture new Pokémon just yet, but you can take this opportunity to build your Pokémon's experience levels. If your Pokémon enters too difficult a battle, use the Run command to escape. If it faints, head home to get a little TLC from Mom, or continue onward to Viridian City and enter its Pokémon Center.'

Cross the Wilds to Viridian City
You begin your journey at the bottom of route #1, and must travel north. There's not a lot of things to do on the way to Viridian City. Wild Pokémon abound, but without any Poké Balls of your own, they're not worth much except EXP. Be careful they don't wear you down, and stick with your damage-dealing regular attacks.

To avoid the fights altogether, minimize the amount of time you spend in the grassy areas. They're the only areas where wild Pokémon lurk, so it's the only time you're at risk of being attacked.

Don't forget to talk to the first guy you pass for a free Potion!