The region around Paris is called the Ile de France. One of the most densely populated in the country, it is also very large and goes far beyond its historical limits. For example, numerous areas listed in Ile de France should normally be in Champagne.
This region is full of interesting places to visit. There are numerous former castle domains all around Paris, from Sceaux or Saint Cloud to Rambouillet and of Course Versailles.
There are also large forests like the one around Fontainebleau and valleys dotted with ponds along the Loing or Essone rivers. Even in the most densely urbanized areas, you can sometimes find interesting places such as the lake of Creteil or the Bois de Vincennes.