Chatsworth is England's most impressive occupied country house, and it is genuinely staggering in scale, the collection includes work by Rembrandt, Reynolds, and Veronese; the gardens were designed by Capability Brown and Joseph Paxton; the cascade waterfall runs 200 metres down the hillside. The Duke and Duchess of Devonshire still live in part of the building.
The farm shop and Cavendish Hotel nearby are excellent. Allow a full day if you're doing house and gardens. The garden alone takes two hours properly. Come in autumn for the colours on the cascade and the kitchen garden.