An easy half-day with children — a short train ride, one big open-air museum and a small, walkable town — but it is cobbled, hilly and short on things aimed squarely at under-fives.
The Skanzen and its little train
Ages 6 to 26 pay 2,000 Ft against 4,000 Ft full price, rising to 2,500 and 5,000 Ft on festival days, and the train that links the regions of the site is a separate 1,400 Ft (1,200 Ft discounted). Open Tuesday to Sunday, 09:00–17:00; the walk between regions is long, so the train is not just a treat.
The HÉV ride itself
For small children the forty-minute suburban train from Batthyány tér is half the outing. Buy a BKK single at 500 Ft plus the supplementary HÉV ticket for the stretch beyond the city boundary, 600 Ft on the 30 km band.
Cobbles, steps and pushchairs
The old town is cobbled and the climb to the hilltop church is stepped and steep. A carrier beats a buggy here, and the flat riverside promenade is the fallback if you have wheels with you.
Visegrád, further up the river
Half an hour on up the Danube Bend, a hilltop citadel above the river's great curve with Renaissance palace ruins below it. It is the castle-shaped day out that Szentendre itself cannot provide.
Come midweek, or after 4pm
The coach parties dominate the middle of the day and the town is far better once they have gone; April to June and September are the calm months. Summer weekends and the Advent market are when it is least pleasant with a small child.