Ah, Amsterdam... My favorite European city. Amsterdam was my first trip to Europe too and even now, having been to many other places from Iceland to Italy, I can think of no better place than Amsterdam to acquaint oneself with the wonders of this fine continent.
Here's a little walking tour for you. I call it the "Best of Pedestrian Shopping in Amsterdam." Start at hopping hangout area Leidseplein, and proceed toward the city center on Leidsestraat. Continue straight (the street may change names) until you reach Koningsplein. Then follow the short Heiligeweg (Holy Way; a good Amsterdam research project is to find out how the street got that name) to Kalverstraat, one of Amsterdam's premier pedestrian shopping streets. Go left on Kalverstraat and follow the street up to the Dam square, where you will find the Koningklijk Paleis (Royal Palace) and Niewe Kerk (New Church). "New" is a relative term in Europe; the New Church dates from 17-something. From the Dam square you have two choices: Continue up the main road Damrak, home of the Sexmuseum, to Centraal Station, or walk on the pedestrian street Niewendijk until you reach the Niewezijds Voorburgwal, where you can make a right and get to Cetnraal Station that way. Whenver I'm in Amsterdam I make this trip on foot several times and never, ever tire of it. Word of caution for the first-timer: Be careful as part of the time you will be sharing the narrow right-of-way with a tram line! Total time: without stopping 20-30 minutes.
Oh, I almost forgot to mention: On this walking tour do be sure to make a pit stop at the Begijnhof (follow the little signs with the arrows). This former convent may sound like just a square lined with houses, but if you've never seen a European residential courtyard designed this way, you will be impressed how far removed it seems from the surrounding hustle and bustle.
Naturally no trip to Amsterdam is complete without at least a brief tour of the Red Light District. If you're afraid of this place just go in the morning; before noon it's mostly tourists milling about. If you're embarrassed you can do a little self-deception and convince yourself you're really just passing through on the way to the Oude Kerk (Old Church). Quite honestly my most lasting impression of the Red Light District is the historical air about the place. As you walk up the surprisingly narrow Warmoesstraat, it's hard not to imagine hordes of debauched 17th-century sailors and the wild nights out that must have been had way back when.
Castles? None that I know of around here, I'm afraid. The flat Dutch countryside doesn't lend itself to the hilltop fortifications of medieval lore. Don't worry, though. You'll have enough to see that you won't miss the castles.
A week too much time? Well, for those whose ideas about European travel come from package tour brochures anything more than 24 hours in one city sounds like a lot; I don't thing a week in Amsterdam is overdoing it at all. Remember, the slower you travel the more you learn. On a first trip to Europe it's tempting to cover as much ground as you can, but you will thank yourself later for taking the time to soak up the atmosphere.
That said, during a 7-day stay I would plan one day trip, just for a change of pace, to a destination of your choice. A number of other spots in the Netherlands have already been mentioned; Belgium is another popular choice (and has the best chocolate and the best fries you ever will find):
Antwerp - 2 hours
Brussels - 3 hours
Brugge - 4 hours
I've just gotten out my train tickets and here's what I paid for these kinds of trips a month ago:
Brussels -> Antwerp EUR 5.40
Antwerp -> Amsterdam EUR 26.40
Brussels -> Brugge EUR 10.30
Keep in mind there are usually discounts for inter-city train travel on weekends. Under no circumstances should you buy European train tickets in the USA; the markup is huge. When buying train tickets in Europe you will get second class unless you ask for first, which really isn't necessary. (Been there, done that, not worth the premium on these short journeys.)
For your remaining 6 days I would play it by ear. If you like museums you can easily spend 3 days just touring those. Use your time to explore and get to know the place. If you do feel like going somewhere else it's easy enough to pop into Centraal Station and get on a train.
Finally a word about the Anne Frankhuis: This place has long lines (even early in the morning on a weekday during the off-season I waited over half an hour) and on the inside is, well, a house. If you go here because you desire to see this spot of such historical importance, that's fine. If you're going just to get the feeling of crossing a required sightseeing item off your list, you may want to reconsider. If your only motivation for visiting is because it's something you're "supposed to see" while in Amsterdam, you could do with skipping it. Just my two cents.
Sorry for the length, but Amsterdam has so much to offer the first-time visitor to Europe that it's hard not to go on and on. I hope I've provided you with information you can use, and that you enjoy your trip.