My husband and I, young seniors, have 15 days to spend. We are planning to arrive in Amsterdam, and fly out of Berlin. We are seeking suggestions for a third city to explore. We also need help in allocating days in each stop. We enjoy beautiful towns, cafes, good food. markets,and strolling through interesting neighborhoods. I am open to, and would appreciate feedback and many suggestions for this trip.

Several posters have mentioned Hamburg as a good destination for a few days between Amsterdam and Berlin.
Easily reached by train.

http://www.bahn.com/i/view/index.shtml

I did look into Hamburg, but it appears to be a big city. Since I will be going from Amserdam to the large city of Berlin, I would prefer to spend my time enroute in a smaller, perhaps more charming, area. I really would appreciate more suggestions. Thanks all.

Amsterdam to Brugge as a base in Belgium then on to Berlin assuming you just want one other city in which to stay.

If you are looking for colorful small towns between Amsterdam and Berlin, check out Quedlinburg, Wernigerode and Goslar in the Harz mountain area. 

Quedlinburg is a restored medieval hill town that looks like a flattened wedding cake with a chocolate abbey crowning at the top. The town is over a thousand year old with over 1200 half timbered houses. http://www.ggramer.de/harz_album/photos/photo_12.html

Wernigerode has always been a polished hilltop jewel since the DDR time when it used to be the show off town for visiting VIPs.  There is a storybook castle sitting high above the town with a commanding view and interior that is well worth a visit.
http://www.wernigerode.de/index.php?id=146004001119i

We enjoyed our hotel stay in the Kaiser/emperor city of Goslar (flat, no hills) 
http://www.goslar.de/english.html
We had 3 nice large rooms overlooking the main city square at the historical inn Kaiserworth but it also has cheaper/smaller rooms. There is an impressive circular stairway but no elevator.