Upon exiting the Metro you will be just across the street from the Chateau de Vincennes. The Chateau is essentially a mini-Versailles with a medieval castle to go along with it – and one of the few fully preserved Donjons (or Keeps) in all of Europe. The grounds were once a royal residence complete with administrative buildings, royal residences, and its own cathedral - all of which is still intact.
The Donjon has a rich history including being a prison during the French Revolution (Mirabeau was briefly jailed here), headquarters to chief of the French Army at the outset of WWII, and SS headquarters during the German occupation.
It's a fascinating place to visit – and the grounds offer a lovely place to sit on the grass and read a book too. Entry to the Chateau is free – and €8 to go inside the Donjon and Cathedral. And not only is it an interesting place to visit, it also happens to not be inundated with foreign tourists; yet.
Adjacent to the Chateau is the immense Bois de Vincennes - essentially a giant park - which includes 4 lakes, a zoo, and miles and miles of scenic paths and picnic areas. This is where Parisians come to escape the city - and at three-times the size of New York's Central Park you will find it quite easy to have a little elbow room and breathing space all your own.