Spreewald is a good bet...there are many towns that are linked together on all these canals and water ways...you can rent canoes/kayaks relatively easily and inexpensively...great for picnics, day trips, big groups, etc.
Teltow-Fläming...many hiking, biking, skating/blading trails with lots catering to such activities.
Take an ostsee ticket (you can take up to 5 each ticket) early saturday morning up to Rügen or Usodom, perhaps with bikes...bike tour, eat fresh seafood, lounge on the beaches, swim...be back in berlin by saturday night around 9:30pm Great, painless getaway.
Dresden, Leipzig, Weinmar...Jena is also neat area. The Harz Mountains...
obviously a little closer is Potsdam, Babelsburg (all rennovated, very nice, playground for rich and famous with many pockets of interesting boutiques, cafe's, sightseeing, activities, etc.)
a bit further from Postdam, is Werder...neat Island Town, also reachable by Ferry.
Wannsee, one can take the BVG Ferry over to Kladow (about 1 hour) with your bikes or without...i prefer the bike trails going all the way back up the Havel.
Something for you hikers and history enthusiast alike: tour, freely as you wish, an old abandoned Soviet/DDR Military Flughafen:
look on google maps where 111 (96n) intersects the E26 Berliner Ring...just north of the ring, south of Oranienburg...it's all open and easily accessible...been out there and spent hours...dont be surprised to see some of the ammo dump bunkers open, with mess kits, gas masks, etc. Very cool experience. (see below)