After defeating a giant robot with a tank, you find a strange Monkey Grotto in Yucca Desert.
Explore Monkey Grotto
There are no enemy encounters here. Go east as far as you can go, then go southwest, then west. Go north through the hole in the wall, then go east, then northeast, and finally west. Step on the hole to go down.
Go west until you find a PSI Stone. Then go east, then south when you can. Follow the path until you find another PSI Stone. From there, go southwest, through a hole in the south wall, and go southwest from there (stay on the left side of the wall). When you can't go farther south, go west, and follow the path. When the path splits, keep going southwest, and go west when you can. Talk to the monkey to get a Quick Capsule.
Keep going west to find a PSI Stone in a corner. Go east past the wall, then go north through an opening in the wall. Go northwest from there, then northeast until you reach the north wall. Go east from there and follow the path to find a hole. Step on it.
XX Cave 3
Follow the path to find the pink spire, and use Telepathy on it to go to Magicant. Then go to the Crystal Cavern to leave Magicant as usual. Since you went to Magicant from XX Cave 3, you will emerge in XX Cave 4 (a new location beyond Yucca Desert) every time you exit Magicant from now on. This is helpful because it allows you to go past Yucca Desert whenever you leave Magicant.
Go east to find train tracks. Keep going east along the tracks to find a train station. Don't go inside. Instead, go south through the trees near the train station, then go southwest along the path between the trees. Eventually, you will reach Youngtown. Go through the hole in the fence to enter the town.