Hi, I lived in The Netherlands for 23 years and for the past 4 years until moving to the US I lived in The Hague.
Some remarkable city's to visit are Amsterdam, Delft, Nijmegen, Maastricht and Utrecht (old city centers, great architecture and history).
Or if you are more into shopping, Rotterdam will do too.
When you are in The Hague, make sure you visit "Het Binnenhof" (seat of the government), "het Mauritshuis" (museum), Palace "Noordeinde", the beach "Scheveningen" and the large churches. Maybe a trip to miniturepark "Madurodam would be nice too.
If you get the chance, take an evening off and have a drink on "het plein" a square in the middle of the city with lots of sidewalk cafes.
There are many more places you can visit in the other cities, probably too much to see all in 1 week. Go to the VVV (tourist information center) and ask for guides to the cities. They will give you much information.