From the centre, walk to the massive blue-and-gold-roofed church just south. From here on, walk south on the Mynais'ka St. Continue on this street until you reach a good place to stand, just before the suburb of Mynai. The Mynais'ka St. will eventually turn into a big street towards Chop and Hungary.
North-West towards Slovakia
Walk straight away from the train station main exit (westwards). After about 300m you find a big bus station. In the house at the service terminals you can get a ticket to e.g. Vyšné Nemecké, which is just behind the border on the E50, for about 18 Hrivni (1,80 Euro), or Michalowsky for about 40 Hrivni. You will recognize the bus because it is slovak, white-blue, very big, modern and got latin letters on it. If you do not want to use the bus you can also just walk for maybe 5km. Ask for the border (межа=Mezha).
Places to avoid
Don't hang around the train station at night, as the police will annoy you, ask for train tickets and passport. They also won't allow you to fall asleep on the chair. Best to go somewhere into a quiet street, or sit near the church just north-east of the centre.
Accommodation and Sleep
Uzhgorod opened its first hostel this year (2011).