Pokémon Gold and Silver/Pewter City

'In Pewter City, you will fight Brock, your first Pokémon Gym Leader. The Pokémon he uses in battle are strong. If necessary, build up the experience of your own Pokémon by having battles in the wild. Before you do either, visit the Pokémon Center in Pewter City, so if your Pokémon faint in battle, you'll resume your journey there, instead of far away.'

Catch the legendary
While you're in town, in Silver Version go into the top right portion of town and talk to an old man with blue hair. He will give you Rainbow Wing, which you can later use to capture Ho-oh in the Tin Tower back in Johto. In Crystal Version an old man facing the route pointing east will give you Silver Wing, which can be used to capture Lugia at Whirl Islands. In Gold Version, there is a man standing next to the Mart who will give you SILVER WING which is necessary for capturing Lugia.

More berries
In the northeast of the city there are 2 berries. Ice Berry and Mint Berry.

Trade opportunity: Gloom for Rapidash
In the Poké Mart, the man standing by the computer is looking for a. He is willing to trade a for it.

Trainer Battle: BROCK
Both Brock and his Junior Trainer use Rock-type Pokémon, and your only chance at victory is to face Brock and his minion with Grass, Water, or Fighting-type Pokémon of your own.

If you defeat Brock, he'll give you the Boulder Badge, which grants your Pokémon a small power boost.