The kids can take a ride on the children's railroad, which runs through the Buda Hills and offers the most scenic views of the city (just over 300 HUF for kids and 900 HUF for adults).
Budapest also has an amusement park with very inexpensive rides - Vidam Park. And, of course, Aquaworld, one of Europe's largest indoor water parks (in addition to slides and pools, there are about 20 different saunas, jacuzzis and even a sauna).
By the way, if you stay at a Ramada Resort hotel adjacent to the park, you can visit Aquaworld anytime for free.
You can also go to:
"Oceanarium" in the shopping center "Campona" - one of the largest in Central Europe (8 halls, each dedicated to a different region of the planet). Tickets cost from 2500 HUF for adults and 1800 HUF for children.
Sugar! is the biggest candy store in Budapest (hundreds of kinds of caramels, dragees, cakes, ice cream and other sweets). "Mecca" for sweet tooth you will find at Paulay Ede, 48. Another sweet treat for kids in Budapest is the Marzipan Museum in the suburb of Szentendre.
Budapest Zoo is a 12-hectare collection of hundreds of rare species of mammals, fish and reptiles. The city zoo is considered one of the oldest in the world - it was founded in 1866. Be sure to visit the Oriental-style Elephant House (with a minaret as a viewing platform), the Palm House (dedicated to tropical nature), Primate World and the Arctic Panorama.