Welcome to Amsterdam!

Amsterdam is my home town, but reading what the others wrote you already had some excellent advise, there is little I can add! So I looked somewhat deeper into your question about castles. There are several castles in the direct neighbourhood of the city, and I wanted to advise you the Muiderslot (anno 1280) in the cozy old village of Muiden (12 km east of Amsterdam), but that castle turns out to be only open for the public April - October.
Then I realized that I, along with everybody else on this thread, forgot the obvious: The Royal Palace on Dam Square, in the hart of Amsterdam, on a walking distance from the Centraal Station. Thanks to the fact that Queen Beatrix only uses this palace a couple of times a year for royal banquets, (she works in Palace Noordeinde and lives in Palace Huis ten Bosch, both in The Hague) it is open to the public almost year round.
More info on:

http://www.koninklijkhuis.nl/UK/palaces/palaces.html

and:

http://www.bmz.amsterdam.nl/adam/uk/groot/paleis.html

Welcome in Amsterdam, hope you have a great time!

Crime: Though Amsterdam's crime rate is dropping, it is still not one of the safest cities in the EU. Crime rates in the EU are usually lower than in the US, but please look well after your belongings and beware of pickpockets.

Tipping: The Netherlands have a reasonable minimum wage. Tipping is appreciated, but not obligational. The waiter won't starve if you don't give a tip. If the service is good, you give a tip, usually about 10 %, if the service is not OK you're not rude when you don't give a tip. Be relaxed.

Amsterdam is an international city, completely used to having foreign tourists around. Including Americans. Most Amsterdammers are friendlier to Americans than to people who won't speak English. The Dutch have learned school-British English at school and know American English mostly from films or through friends. Sometimes there are small misunderstandings. On most people, a friendly smile helps.

Again, have a great time!