I’ve been taking my kids to Budapest since they were about that age (they are all through college now). They always enjoyed it. The boat rides, the bath houses, the zoo, the parks, the puppet theater, the great majestic old buildings, the train rides, funicular, ferris wheel, etc. This is about the best site i have found yet for family events in Budapest
I’ve done just about all of it and it’s been fun for the old guy too.... Ive been to Prague too, and i think you and the kids will enjoy Budapest a lot more. Fewer crowds of tourists and fewer drunks.
With 2 or 3 nights, choose from the list (from another post):
Five nights in Budapest doesn't leave much more time than maybe a day trip. Vac is great for the second day trip, but for the first (and the only) I think you would get more out of Szentendre. Pecs, Eger, etc, a bit far for a day trip.
1st day, FIRST NIGHT: If you are coming from Salzburg you probably aren't reaching Budapest till mid-afternoon (unless you like to get up really early). With four kids, between checking in and getting settled down, maybe its possible that you only have some part of the early evening to explore Budapest. I would suggest staying up on Andrassy ut someplace as it's great for wandering around with the kids and there is plenty to see and do for a family trip. Couple of decent Pizza places on Andrassy ut. Also some good burgers just behind Andrassy ut. Maybe the kids would like the Miniversium? (on Andrassy ut)
2nd day, SECOND NIGHT: Okay this day is a full day. Lets say you do Buda and a small part of Pest. Maybe go to the Circus in the evening (at the end of Andrassy ut).
3rd day, THIRD NIGHT: Maybe a Day trip to Szentendre and ride the boat back. Kids should like that. Maybe the Széchenyi Baths in the evening (at the end of Andrassy ut)
4th day, FOURTH NIGHT: The other third of Pest and maybe a picnic and running around on Margaret Island. (Andrassy ut to the 4/6 Tram - 3 stops). Possibly the Puppet Theater in the evening (on Andrassy ut)
5th day, FIFTH NIGHT: The final third of Pest and boats on City Lake (on Andrassy ut)