Yes, I know. You come for the food......
Typical for Aquitaine is that you fill find many different things in a concentrated area.
Feels like I'll need a lifetime to explore everyting. Some topics might be the sea and the beaches, the mountains, wine, festivals, shopping, travelling with children, skiing and other sports, taking it easy, eating fantastic food...
If you are going for the sea and the beaches, I'd split the coastal area in four parts or even five:
1. The north part of the Silver Coast, close to the Arcachon Bay and Bordeaux. Here you have the excellent wine region Medoc close by but it gets pretty crowded in summer.
2. The middle part of the Silver Coast, the least known and the most untouched, vast views and lots of space. Perfect to take it easy, enjoy the sea and go biking in the pine forest. Calm.
3. The south part of the Silver Coast, with a more urban feeling, closer to the Pays Basque, Spain and the Pyrenees mountains. A good compromise between sea; sand and civilisation.
4. The Basque coast and a more dramatic coast with beaches and cliffs mixed together. Houses all the way down to the water front, strong Basque culture and of course very close to Spain. Very crowded in summer.
5. I add a fifth one which is not the sea but the big lakes close to the sea. They have calmer beaches and are a good option for families with children. Still close to the sea and lots of good camping options..
If you want the mountains:
Then the Pyrénées Atlantiques is the perfect option, either the Pays Basque, busier and on the seaside, or Béarn, in the countryside with rolling hills and real mountains. Pays Basque is getting a lot of tourists while Béarn is very calm and good for hiking and taking it easy.
If you want culture, food, shopping and wine there is really only one answer:
Go to Bordeaux! Perfect for a cultivated stay, a romantic getaway, great shopping and an atmosphere that reminds a lot of Paris. Pick one of the 600 restaurants to get a top notch gastronomic expericene or an easy bite at a genuine brasserie. Museums, theatre, music....
(But I wouldn't stay more than a day or two with small children).
If you are a wine nerd:
Aquitine is heaven on earth for wine interested persons, and I don't only think of the world famous Bordeaux region... have a look at Madiran, Jurançon, Bergerac, Irouléguy or the Vin des sables from Capbreton.
Party and music:
Go for one of the festivals in Bayonne, Dax or Mont-de-Marsan. Perfect if you're 20 and in good shape, it takes a lot of energy to participate for five days in a row! Elderly people might be contented after a day or night... Else try the Music Festival, a national event in France end of June.
... and food ....
Travelling with children:
General for Aquitaine is lots of activities linked to nature and outdoors. Spending time by one of the big lakes, enjoying the beach and the huge waves (surfing from six years), biking in the pine forest. Lots of child friendly activities like obstacles tour in the trees, canoeing, horses, animal parcs and amusement parcs.
We've done lots of visits at wine castles, which the children enjoyed a lot the first times. Look at the grapes and the fields, taste some, go down the cellar and see all the weird equipment can be very exciting for children. (Our children have unfortunately been over exposed and almost refuse these visits by now... oh no, not another wine castle).
Lots of good campings by the sea, very child friendly and well situated. Station Kid is a quality label for child friendly places (like Hourtin, Carcans and Mimizan for example).
The Pyrénées are not of the same size as the Alps, but you get good value for your money, especially families with children. And the food is good...
Doing nothing:If your main aim is to get rid of stress I would recommend the inner parts of Aquitaine. Very nice landscapes, rolling hills and vast fields, cows and ducks. Very idyllic and free from tourists. Rent a house, go to the local markets and enjoy eating local produce.
Getting excellent food:
Trust me, you get good food everywhere, but not always the same. The different areas have regional differences. More refined restaurants are more likely to be found in Bordeaux (but be aware, some of the top Michelin star restaurants are in hidden places). The Arcachon Bay is of course a good place for oysters and seafood (they breed oysters there). The Basque cuisine is very well known and inspired by the Spanish cooking. In Landes you'll have a lot of duck and Armagnac...
... and the wine!!