Bratislava for kids
Bibiana is both cheap and very, very good for kids. They have exhibits about famous authors or art ideas that are educational but at the same time interactive and fun. Recommended for the younger ones especially.
There are many awesome places to swim. Almost all of them have some special things for kids. For example, the water park Aulandia right in the city has a shallow pool with three short slides. The outdoor pool at Rosnicka has a special pool for children under six
and a decent playground.
Around Bratislava it's a good idea to do hiking and other outdoor things with your family, mostly for sturdier children. Koliba is a nice place, because there's always something to do, like skiing in winter or the toboggan slide, pony rides and hiking in the summer. The Devinska Kobyla is a very long climb with a great view at the top, but if you have younger children you might want to try instead the giant sandstone Sandberg near Devin.