Let KAYAK do the searching
Based on KAYAK hotel searches, the most popular destination is Le Mont-Saint-Michel (47% of total searches to Normandy). The next most popular destinations are Rouen (25%) and Bayeux (19%). Searches for hotels in Lisieux (9%) are also popular.
KAYAK users have found double rooms in Normandy for as cheap as $50 (Cherbourg-en-Cotentin) in the last 3 days. The average price is $289.