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. Route #1 is very peaceful, and doesn't contain many interesting features. As a result, there's not a lot of things to do on your first trip to Viridian City. One of the first people you will encounter is a man who offers you a free Potion. Don't miss out on that.

Wild Pidgeys and Rattatas abound, but without any Poké Balls of your own, the only thing fighting them is good for is EXP. Be careful that they don't wear you down, and stick with your damage-dealing regular attacks. To avoid the fights altogether, spend as little time as possible walking through 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.