If you head directly north from the topiary garden of Striaton City, you will find a preschool and a pokémon Day Care. The Day Care can take care of two of your pokémon at a time, which means that you can make pokémon eggs here.

Inside of the preschool building, one of the Nursery Aides will heal up your pokémon for free if they are hurt. There aren't any trainers inside of the building, so you can just go around and talk to the kids and other Nursery Aides.

Outside, in the playground, a Nursery Aide will challenge you to a match, as will all of the preschoolers in the playground. They're all pretty easy to defeat.

To the west of the stairs to the preschool, there are twins who will challenge you to a match.

Continue west, and you'll bump into Cheren, who will want a battle. He has a Purrloin and his starter.

After the battle with Cheren, some Team Plasma grunts will run past, followed by Bianca and a little girl. It turns out that Team Plasma "liberated" (in other words stole) the girl's pokémon. When you follow, you'll find that Cheren is outside of Wellspring Cave, and he is waiting for you to heal up your pokémon so that the two of you can go in and fight Team Plasma to get the girl's pokémon back.

Once you're ready, go into the cave. When you get close to Cheren, the two of you will set aside your friendly rivalry to fight a double battle with the Team Plasma grunts. They have Patrats, and Cheren will use his starter.

Once you defeat the grunts, they will give back the girl's pokémon and run off. Go outside and find the girl to return her pokémon. In thanks, she will give you some Heal Balls. Cheren will head south to Nacrene City.

Before you continue on, be sure to check the path just east of Wellspring Cave. There is a trainer in the grass, and there is also an item south of that trainer. Be sure to look around Wellspring Cave, also, because there is an item that you can reach in there. You can't really do much else in the cave, though, except catch the pokémon that are there, like Roggenrola, Woobat, and in swirling dust spots, Drilbur. You'll be able to do more in the cave once you have Surf.

Now you can head south from Wellspring Cave. There is more to Route 3 that Bianca wouldn't let you explore until you rescued the girl's pokémon. There are some School Kids here, and an area of tall grass. Cheren warns you that in the tall grass, you might have to fight double battles against wild pokémon. There aren't any items in the tall grass, so you can just leave it alone if you want to.

Past the bridge, you will find a building that leads to Nacrene City.