There are three garden areas in Burghley house, the garden of surprises, the sculpture garden and the more formal house gardens. The garden of surprises is an interactive area, where visitors of all ages can paddle, dodgy and splashing in the various water features. It isn't an overly large area so I imagine it would get quite busy on really sunny days. It could also be improved by adding some colour. However, the teenagers enjoyed pushing each other in to the water and the toddlers enjoyed paddling about and the adults, well we revered back to being children and splashed about as much as the rest.
After a picnic we decided to go to the sculpture garden, this has been at Burghley a while and every time I go there seems to be new things added. There is a very pleasant walk round and the sculptures are interesting to spot and look at. It is a shame that your not allowed to touch and play on the sculpture, as some of them are very tactile and are just asking to be climbed on. The views over the lake are beautiful.
I think if you are visiting the best thing is to take your time, enjoy the marvellous surroundings and let the kid in you come out.