From the railroad tracks you used to walk to the desert, continue to follow them along until you reach the Youngtown Station. Continue heading south and eventually you'll reach Youngtown itself. Make sure you buy the Air Gun from the shop for Loid as it's his strongest weapon in the game, then check out the house on the western side (the one that has a baby in it). Use Telepathy on the baby and both Ninten and Ana will learn Teleportation, which allows you to visit any previously visited town you'd like, provided you have the space to use it (you'll see what I mean when you actually try to use it).
That's really all there is to do in Youngtown, so head to the east of town and cross the bridges you eventually come across. Soon, you'll find a house along the way. Its resident? None other than Pippi! Also, Loid's dad is outside the house in the garbage can, talk to him if you'd like. Thanks to Pippi being in this particular location, you may feel free to train to your heart's content as she offers free healing, making this quite a convenient little spot, provided none of your party dies, in which case you'll have to go to Magicant. Thankfully, now that you have Teleportation, getting back to Youngtown won't be any trouble at all!
Once you feel you're sufficiently leveled enough, continue along the bridges south-west from Pippi's new house and you'll wind up going east. Once you start to see trees, follow them north until you get to another bridge. In time, you'll find a bridge that goes west with a dirt path on the other side. Follow it and you'll find yourself in Ellay.