The Van Gogh Museum is a must. The Rijksmuseum is also amazing. Amsterdam is an amazing city to visit, we returned there many times. If you want to see the countryside, I second going to the Zaanse Schans, only a short train ride away.

I always rent a car to go visit the Kröller-Müller Museum (for more Van Gogh) at the Hoge Veluwe National Park ( http://www.hogeveluwe.nl/en/14 ) where you ride bicycles in the beautiful trails. Of course you can get there by train, but I never did.

Have a wonderful trip!