Searching for holiday accommodation in Budapest

Hello,

I will be traveling to Hungary with my two kids (8 and 6) and therefore I am looking for a good and low budget accommodation in Budapest April 10th till 14th. Can anyone recommend "something" with enough place for three? Central location for trips within the city would be great, so we do not need to use the car.
Since my parents are hungarian origin, I can speak hungarian. So communication in hungarian language there would be possible.

Oh and any recommendation for things to do and see with kids in Budapest? :-)

Thank you!

Cheers,
Aniko