The canals, bridges and houses
The Amsterdam city center is girdled around with several canals. Heren- Keizers- and Prinzengracht are probably the most famous and elegant ones. Notice the different facades of the canal houses and how small (but very deep) they are. The smaller, the less taxes needed to be paid. Behind the houses are beautiful gardens.

Beguine houses
Early 14th century a group of women lived here dedicating their lives looking after the sick. These small, typical Amsterdam-type, houses were once surrounded by water (swamp). Later a part of the swamp was filled up so new houses could be build. A place to calm!
You can enter via the gateway Gedempte Begijnensloot.
http://www.begijnhofamsterdam.nl/index_engels.html

Vondelpark
Almost in the city center you will find this large and best known park of Amsterdam. It's a recreational area where you will find many locals as well as tourists relaxing, jogging, playing, biking etc. A nice thing to do is to arrange a picnic here. But there are nice restaurants (like Vertigo) as well.

Rembrandtplein - Rembrandt square
A big square surrounded by many hotels, restaurants and cafés. This is a good spot to hang out in the evening. And of course on sunny days...sit on one of the many terraces and watch the people go by.
In the middle there's grass with the statue of Rembrandt.