Because of the investiture of King Willem-Alexander of the Netherlands on 30 April you won’t be able to visit the Royal Palace in Amsterdam, nor the New Church for some time. The royal palace closes after 7 April and will only reopen on 7 May. You however have to check their website anyway when you would like to visit, as they are closed quite regulary. The New Church even closes its doors on 2 April because of the preparations for the investiture. And to me it is not clear yet when they will exactly reopen.
However nobody has to get the idea there is nothing royal to do in Amsterdam anymore, see also my post about royal exhibitions. Also the Beurs van Berlage in Amsterdam, where the future King and Queen of the Netherlands celebrated their civil wedding on 2 February 2002, has a royal exhibition: “Onze Koningin” (Our Queen). From 12 March to 25 May 2013 you can admire 145 pictures of Queen Beatrix of the Netherlands there, from the archives of the press agency ANP. It shows pictures from her 33 years as Queen of the Netherlands.
Another location with a royal history is the Westerkerk. This is the church where in 1966 Queen Beatrix married Claus von Amsberg.
If you have some time left, visit the Museum Van Loon. This beautiful house on the Keizersgracht in Amsterdam is in the possession of the Dutch noble family Van Loon since 1884. The last member in male line jonkheer Maurits van Loon, died in 2006. He opened the house for the public in 1973. His widow Martine van Loon-Labouchere – Mistress of the Robes of Queen Beatrix – still lives in the house. His daughter (from his first marriage) Philippa Colomb de Daunant-Van Loon is president of the museum foundation.
But of course there are lots of other things to do in Amsterdam. Just have a look here.