I had a look through the European hotels featured in the Conde Nast Top List Hotels 2008 and found only one establishment in the lowest price band of under $200 a night. It's L'Auberge Basque which is located near St Pee sur Nivelle, in the south western corner of France close to the Atlantic Coast. L'Auberge Basque is praised "as an edgy mix of urban good taste and farmhouse Basque".
© CanonS2
The coastal spa town of St Jean de Luz is the nearest large town. The Basque region straddles France and Spain so it's a short trip over the border into Spain and the city of St Sebastian with it's three beaches and array of restaurants.
Are you influenced in your choice of accommodation by recommendations such as the Conde Nast Hot List? I wonder if there will be any room at the inn at L"Auberge Basque after the publicity, unless you book in low season or two years in advance. I wonder if it will spoil part of the charm of L'Auberge if it is over run with Conde Nast disciples? Perhaps one way to reduce demand might be to increase the price (although I doubt if that will deter the Conde Nasters) in which case there will be no European hotels in the Hot List at under $200 a night.