Upon arriving in Cherrygrove City, an old man called the Guide Gent will approach you and then show you around town. He’ll show you the Pokémon Center, the Poké Mart, and the ocean. However, he runs pretty fast (pretty good for his old age!), so he gives you a set of Running Shoes after he’s shown you around town. Now you can run by holding in B! You can also tap the little shoes on the bottom screen to make it so you run automatically, without having to hold in B. Pretty handy!
You can heal up your Pokémon in the Pokémon Center if it is low on HP. I’d recommend doing that before heading north, to Route 30.
In the Poké Mart, you can buy a Potion for [pd]300, an Antidote for [pd]100, and a Parlyz Heal for [pd]200. You can’t buy Poké Balls just yet, though.
As you try leave town to Route 30 to the north, you’ll be stopped by the energetic old man again. He’ll give you the Map Card for your PokéGear, allowing you to view the map of Johto when you use your PokéGear. You can zoom in and make notes on locations if you have the desire to, though the notes probably won’t do you that much good now.
Now head on north to Route 30!
[link to Route 30]