Cerulean City is home to the second Pokemon Gym. The first thing you can do is heal up at the Pokemon Center in the middle of town. If your bag is getting a little full, make sure you deposit some items in the PC. You can also sell some unwanted items at the Poke Mart and buy some more Potions and Poke Balls.
A girl in the house to the left of the Pokemon Center is looking for someone to take care of a Bulbasaur. She will give you this Bulbasaur if your Pikachu likes you enough. Hopefully, you have been using your Pikachu in battle, giving it items, and not allowing it to faint in battle. Getting Pikachu to level 20 should be enough. You will also need an extra slot in your party before you can obtain the Bulbasaur. It will be a great addition to your team for the upcoming gym battle.
The Cerulean City Gym is located to the right of the Pokemon Center. You can challenge the gym now if you think your Pokemon are strong enough, but I recommend training up a bit at the two routes to the north. Before you can go to the routes to the north, you’ll have to face your Rival. Make sure you’re ready for a tough battle.
Your Rival will have four Pokemon at semi-high levels. Spearow has a strong Peck and Fury Attack. Rattata can do quite a bit of damage with its Hyper Fang. Hopefully your team is around level 17 by now and can withstand the damage. If not, you’ll have to do some training on Route 4.
Peck, Growl, Leer, Fury Attack
Tackle, Tail Whip, Quick Attack, Hyper Fang
Sand-Attack, Growl, Quick Attack, Tail Whip
After the battle, heal your team at the Pokemon Center and continue north to Routes 24 and 25.