Viridian City is a rather small town that doesn’t have much going on for now, but it’s also the first town you’ll find that has two staples for your adventure: the Pokémon Center, which is the large building with a red roof that’s impossible to miss; and the Poké Mart, which is the building with a blue roof to the northeast of that.
You can heal your Pokémon inside of a Pokémon Center by talking to the nurse at the counter. Your Pokémon will be weakened after battling other Trainers, which is something you haven’t had a chance to do just yet, but you will later on. Keep in mind that there is no longer a PC in the Pokémon Center — you can access your extra Pokémon by checking out the Pokémon Box option from the Party or Bag menu, even when you’re not in a Pokémon Center.
The Poké Mart sells items such as Poké Balls and Potions. As you approach it, the shopkeeper will say he has a delivery for Professor Oak but can’t leave the Poké Mart. He’ll give you the Parcel, which you need to deliver to Professor Oak back in Pallet Town. You’ll be given a choice as to whether or not you want to head straight back to the lab — if you say yes, you’ll be teleported back there instantly, otherwise you will have to walk back through Route 1 to Pallet Town.
Three shady characters are blocking your path to the north, so go ahead and head back to Pallet Town really quick to get it out of the way, since you’ll need to do so before continuing anyway.