"The young tourist heads to another city."
Translation:A fiatal turista átlép egy másik városba.
Your translation is perfect.
On "átlép", I can say this much. It can mean a quick trip. I step over to another place to quickly take care of something, and then I'll be right back.
Similar to the English phrase "step out (to run a quick errand)". But this is not what the English sentence says.
Its definitely confusing for a beginner like me. If an idiomatic usage of átlep is going to be shown, that needs to at least be covered in the 'tips and hints' text. Since, in English we can say something like 'hop over' to or 'step out' in the way you mentioned, I got it from context but it was still unfair.
As a hungarian, I would never use atlep to an other city. Maybe in sleng when i atlep to my friend's house. It's really step through.