jacknyoc, thanks for your kind message.
The Netherlands has one of the highest population densities in Europe. Other than farmland, which there is a lot of, there is only the coast, which there is also a lot of, and villages and towns.
Many of the cities and towns here were developed during the Middle Ages and are still not changed very much. Which is another reason that an auto will not help you (you cannot drive into some of these small towns).
If you stayed in Amsterdam, there are a number of places to see that are quite close and could easily be reached by bicycle, bus or train. Aside from the places already mentioned, there is Naarden-Vesting (an old fort town), Muiderslot (a medieval castle:
http://www.muiderslot.nl/english), Monnickendam (a small old fishing village on the water) and Broek in Waterland (a beautiful small village).
All of these would, I think, meet the description you gave and be very enjoyable besides.