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Old city, parliament and the Margaret island.
Once there it all depends on weather. If you are out of luck, enjoy the pampering at the hotel again. You will have another perfect day.
Oldies goldies first
While your kids are still on full powers, visit the Great market hall. It is big. Huge. And tasty. All sorts of food there.
Take a walk across the bridge and walk up to Citadella for the view and some fresh air if you are really for more walking.
In case you have missed it on first day, walk along the Danube river and enjoy the view over Buda. You will see the Budapest whale among other old buildings.
Or else, just follow the Vaci utca and get the best out of old city centre.
The parliament surroundings
At the end you will reach the parliament. But that's just one of the magnificent buildings and stuff you will see. Check for the Hungarian academy of science, Gresham palace, Shoes on the Danube bank or Kossuth memorial.
Relax on Margaret island
Depending on your sports abilities you can take a walk or bus to the Margaret island. There your kids can enjoy some wild time. And you can have a picnic or just enjoy the nature your way. You deserve it and your mind should relax after 4 days of impressions that this great city will lay upon you.
Complete guide
I've packed all the fun into a set of points in this guide. Well, just in case you are hungry and not limited by the diet, enjoy this secret. The best chimney cake in Budapest they say. :)