The Basse-Normandie (Lower Normandy) region of northern France consists of the Departments of Calvados, Manche and Orne making this quite a compact area to explore.
The whole area just oozes history ranging from the Bayeux tapestry to the D-Day Normandy landing beaches. All this is set in charming towns and villages filled with the characteristic half-timbered buildings of the region.
It's a very touristy region and so you'll be spoilt for choice in terms of your accommodation amongst the many rural gites (self-catering/vacation rental) properties and B&Bs.
Amongst the collection of Les Plus Beaux Villages in this region are Barfleur, Beauvron-en-Auge and St Céneri le Gérei.
Although the region is popular it's not particularly well served by airports and your best bet is probably one of the Parisian airports such as Charles de Gaulle (CDG) or Orly (ORY).
Ferries are plentiful in and near the region arriving to Cherbourg within the region but Calais isn't far away.
The rail network is extensive and very practical given the compact nature of the region. You can get the Eurostar from London to Lille and change there.
