As to things of interest for your children Budapest is loaded with first-rate activities, the Zoo in the city park is truly world class. While there spend a few hours just simply walking around the park seeing the castle checking out Hero’s Square or going to Szechenyi Bath (very child friendly).

A couple of other ideas would be the children’s railroad (liked more by the younger kids than older) and while out that way maybe even take the time to ride the Libego (chair lift). The Palace of Wonders is also a pretty good activity, all of these are easily searched here are TA so you can see which may or may not interest you, but all are good fun.

Margaret Island is a great way to spend a day when it is nice outside. You can walk around have a picnic even rent a four wheel pedal cart to explore the island, there is even a nice small petting zoo there and you will also get the Danube views too. Also on the island there is Palatinus Strand (sort of a large outdoor water park) a very nice place to relax with swimming pools and the girls seemed to like it much more than the formal Budapest bath houses since it seemed to be filled with more kids their age.

Kids enjoy riding the public transportation M1 but specifically the #2 tram both at day and then again at night. The route it takes runs right along the river a quite picturesque path that offers you fabulous views of the Buda side of the city with the castle and some of Budapest’s beautiful bridges.

One more fun and kind of unique activity is to have your own Hungarian stamps made at the post office. Oldest to youngets kids will love seeing their picture on a stamp. It's quite cool especially when friends at home get postcards with the stamps on them. Its even fun for grown ups when their friends or relatives get a post card with a custom stamp. Here is the link so you can decide ...

As to markets definitely swing by and check out the Great Market Hall (Központi Vásárcsarnok) also known as the Mecca of paprika; definetely worth a few hours looking around.

These should get you started planning.