If the budget allows try Le Manoir aux Quat´Sasons in Great Milton. It is the only country house hotel in the country to achieve and sustain two Michelin Stars and the Relais and Chateaux Purple Shield.
If that´s too rich for your taste there are plenty of award winning restaurants in the area as well as plenty of hostelries serving good wholesome pub food.
For those making a day trip to the district there are teashops galore just waiting to welcome you and to recharge your batteries ready for the next round of walking, shopping or sightseeing.