[X] Learn about Caving - Seeing the caves around Cerulean City gives you an idea that maybe you should indulge your curiosity. Try and see what you can do exploring the safer parts of the cave system.
[X] Train with Dratini and Pineco - Both of your Pokemon are good in a battle, Dratini having grown through their playdates, and Pineco being rather perceptive herself. Training for a few days would help them grow.
[X] Challenge an Experienced Trainer - The other option to seek out a Pokemon battle would be to go to the Cerulean Gym and challenge one of the attendants there. You may even win.
[X] Learn to Swim - While you do know how to swim, there is a notable difference between swimming for fun and scuba diving. And an even greater difference when it comes to exploring underwater caves. Learning more advanced concepts would be fun.
[X] Challenge Luna - A known trainer with a decently trained Growlithe, she would make for a good sparring partner while you're here. And maybe let you talk in the future.