After catching a few pokémon in Route 1, you go north to Viridian City.
You can explore Viridian City, but there isn't much that you can do there right now. If you want to explore the whole town, don't go up to the blue shop in the east part of town until you are ready to leave.
You can go west to Route 22, where you can catch Nidoran♂, Rattata, and Spearow.
In the southwest corner of Route 22, you will find 5 Poké Balls.
Return to Viridian City
Back in Viridian City, there is a narrow path in the west side of town along a white fence. Keep following this path to a small tree, and check on it to get a Potion.
If you try to go north in Viridian City, you will find the path blocked by a pink haired girl, and purple haired guy, and a Meowth. They won't move, so just ignore them for now.
Get the Parcel
If you go to the blue Poké Mart in the eastern part of town, the Poké Mart clerk will give you a Parcel and ask you to deliver it to Professor Oak. You can choose to go back to Professor Oak's lab right away. If you stay, you can shop at the Poké Mart after the clerk goes back inside. When you are ready, deliver Oak's parcel.