Budapest’s HÉV suburban railway trains connect the suburbs and surrounding towns. They’re the best way to reach Szentendre, the closest Danube Bend town, as well as the royal castle at Gödöllő. Otherwise, it’s unlikely you’ll need to use them – unless you’re turned on by their distinctive green colour.
HÉV schedules are similar to the metro. But do check the timetable if you want to plan your return journey. To keep the inspectors happy, buy a supplementary ticket if you leave the city boundaries (these can be bought on the train itself and won’t cost you much).
Budapest also operates a tram-like cogwheel railway out to Széchenyi hill – a popular picnic and sleighing spot depending on the season. Take the tram for two stops from Moszkva tér metro station to Városmajor. BKV tickets are valid.