We recently visited here for the Cadburys Easter Trail (which was excellent fun even if a little wet), but the Manor and grounds open most of the year. The house is open for part of the year but we haven't yet gone round the house, the grounds are impressive enough.
The gardens are stunning and quite something to walk around, with view points across the county along the way, big slopes that make you want to be 5 again and roll down them, also aviary's home to a collection of exotic birds, garden sculptures and fountains.
The very poplar outdoor playground is wonderful to visit and good for children of all ages and spread across the side of a hill with footpaths between the stages. There is a very lovely restaurant and stables cafe, which sells some amazing cakes. Throughout the year there are regular family friendly events.
All areas are easily accessible for pushchairs and prams http://www.waddesdon.org.uk/