I am seeking recommendations for either museums or gallery districts for viewing contemporary art in Amsterdam. I certainly plan on visiting the Rijksmuseum and Van Gogh Museum, and hope to make it to the Rembrandt house, too. I will purchase a museumkart. My hotel is close to the Ann Frank House. Any suggestions for art/architecture "not to be missed" are most welcome.
About architecture from different periods there is a lot to see in Amsterdam. So not only that famous 17th century centre, but certainly architecture from later periods for instance that of the here better known Amsterdam School or the “Beurs van Berlage”. There are quite a lot of walking or cycling tours on offer also for contemporary architecture, have no experience with them but maybe the next offer a tour to your liking.
http://www.amsterdamcitytours.com/bike-tours.html (€350 is a typo!)
If you like Modernism you can visit the UNESCO listed Rietveld Schröderhuis, but located in Utrecht. However also nice is Jan Duiker´s Openluchtschool in Amsterdam-Zuid.
The Oude Kirk (Old Church) in Amsterdam has changing exhibitions of contemporary art. Here's their website:
FOAM (contemporary photography museum) at Keizersgracht 609 is really good. They stay open until 9PM on Thursdays and Fridays. I believe the Museumkaart still covers the admission. On Thursday nights, you can get a buffet dinner in their cafe (at a really reasonable price) and then a free guided tour of the galleries.
There is also the Eye (film museum). You can take the free ferry located near Amsterdam Centraal train station and boat across the Ij Harbor to get there (and get a water view of the city while on the ferry). Even if you don't particularly care for film, the building that the museum is housed in is pretty cool from an architectural standpoint. You can see their permanent collection for free with your Museumkaart, but if you want to see one of the films they are screening, that costs extra.