With no doubt, Budapest is safe and a child-friendly city. There are plenty places to entertain young ones. Hungarians tend to be welcoming to kids without making them the centre of attention as you might experience it in Italy.
Facilities are a bit patchy, though; while the network of playgrounds is marvellous, nappy-changing facilities (pelenkázó in Hungarian) are hard to find (but we find more & more in last years) – they’re mostly concentrated in big shopping malls. Buildings with their huge gates don’t tend to be very accessible if you’re pushing a buggy, but help is usually quickly forthcoming when for example you’re trying to negotiate stairs.
On public transport people will readily give up seats to pregnant women and to parents with babies. You will also find signs at speacial seats for parents with babies on buses and trams.
Shopping for babies has become much easier in recent years – the big malls are the best bet for nappies, baby toiletries and clothes. Many malls also have indoor play areas for children.
Restaurants usually have high chairs and some even put on activities for children, and although there isn’t a culture of whole families dining out in the evening. In many restaurants you can ask for small child’s portions – called "kisadag" in Hungarian.