Buda Castle LabyrinthCave passages under the castle hill, dimly lit and cool. Around an hour and a half, and better suited to children of about five and up. Cash only.
Budavari Siklo (Castle Hill Funicular)Short funicular from the Chain Bridge up to the castle district, running in wooden carriages. A queue is normal at midday. Free below 3.
Danube River CruiseBoat trips along the river past Parliament and the castle. Evening departures see the bridges lit, and daytime ones work better for naps.
Outdoor space
Gellert Hill and the CitadellaClimb or bus ride to the hilltop above the river, with the Liberty Statue and a wide view over both banks. Steep paths on foot. Free below 6.
Gyermekvasut (Children's Railway)Eleven kilometre narrow gauge railway through the Buda hills, staffed almost entirely by children in uniform apart from the driver. Reached by cog railway from the city. Check timetables, as routes are shortened out of season.
Halaszbastya (Fisherman's Bastion)Terraces and turrets above the Danube with the best view across to Parliament. The lower levels are free; the upper terrace is ticketed in peak hours.
Hosok tere (Heroes' Square)Wide ceremonial square at the entrance to City Park, with colonnades and statues. Open space for running, and the metro stops beneath it.
FreePark
Orszaghaz (Hungarian Parliament)Guided tours of the riverside parliament building, including the crown jewels. Timed tickets, booked ahead, and around forty five minutes. Free below 6.