Hi, I will stay in Berlin during the month of October. I would appreciate to receive your suggestions on best near sites to visit during one full day and up to about 100 km far so as to go back and sleep in my apartment. I will use my own car and due to the fact that probably there is not so much to see in only one place you can also consider to suggest more that one stop during the same one day journey. My interests are 360° wide, from landscape to local traditions and celebrations, architecture and story.
Thank you.


http://www.guardian.co.uk/travel/2012/oct/01/berlin-day-trips-readers-tips
Between 1,5 and 2 hours far are Dresden, Hannover/Wolfsburg, the Baltic sea if the weather is nice.
This German-language website http://www.quermania.de/deutschland/ausflugsziele-deutschland.php allows for a quick orientation in the Länder around Berlin. A lot, if not most of Mecklenburg, Brandenburg, Sachsen-Anhalt and Sachsen will fall within your 100 km radius.
Some random suggestions on my part would be Eisenhüttenstadt (which started its DDR-life as the socialist model city of Stalinstadt), Dessau (for the famous Bauhaus, but also for the parks in and around the city), and Rügen (for its chalk cliffs, the famous KdF-resort of Prora, and the restored glory of its pre-war beach resorts).

nature:
Spreewald (Lübbenau is in the link above), Potsdam(rent a bike and go around Schielowsee (See=lake), rent a ca-yak at S-Bahn station Griebnitzsee or better in Caputh(if rental stations are still open in October).
mix of nature and history/sightes:
Rheinsberg north of Berlin: lakes and castle
Potsdam: lakes and many castles
area of Chorin: monastery Chorin, situated at a lake with nearby lake longish Werbelinsee
Lutherstadt Wittenberg with the nearby Wörtlitzer Park EDIT: the post above lists Dessau which can be combined
As stated above, the Autobahn allows longer trips within one day. The picturesque towns of Quedlinburg(far, can be combined with Magdeburg, Halberstadt or Wernigerode)) or Tangermünde(can be combined with monastery Jerichow and with Stendal) are in range.
I have done some of the day trips by train but by car you're even faster.
Edited by: european83
the website [www.visity.de] is dedicated to excursions around Berlin, just enter your starting point (e.g. ZIP-code of Brandenburg Gate is 10117), radius and select your fancies - yielded both decent and unusual results for me. downside: site works in German only...
further, consider checking the newsletter Germany for more ideas, there are quite some bits on Berlin and surrounds on it.

If you are into skating (biking too but that can be done in many places), there is the Flaeming Skate, about an hour away from Berlin: http://www.flaeming-skate.de/en/home.php
I haven't seen anything like it anywhere, great for one or multiple day tours on skates or bike through typical Brandenburg villages and landscapes. There are also some smaller sights nearby like the Zinna Monastery.