Amsterdam itself is the highlight. Spend some time wandering along any one of the many canals ringing the city and you will understand why: the city is beautiful. And coming from New York City, the contrast is stark: the low buildings and ubiquitous canals contributed a sense of spaciousness to what is actually a crowded city. More importantly, to me at least, was the quiet--Amsterdam is remarkably peaceful. That may have to do with the relative lack of cars in the city (Amsterdammers seem to prefer bicycles).
Quick Tips:
Learn to speak Dutch. Sure, everybody here speaks fluent English, but that's not the point. The point is that it's difficult to remember what street you're trying to get to if you can't pronounce it.
Rent a bicycle, if you can. It's probably the best way to get from place to place in the city, and it lets you see more of the city than you would walking. This is important if you're just there for a short stay.
I would suggest going when it is warm. I would suggest this because I went when it was hovering around freezing, which, by the end of the trip, was really annoying. Mind you, the crowds were probably smaller and the price probably cheaper, so fine, go whenever you want. Just know that you'll want to spend time wandering around the city, and that is best done when it is warm and the leaves are on the trees.
Seriously, though, this is such a great city, I think it would be hard to get it wrong. The best suggestion I can offer is just to visit.Best Way To Get Around:
Bicycle. They're everywhere in Amsterdam and available from several places to rent. Just outside the train station is a sight I had never seen before: a three-deck parking garage just for bicycles! Bicycle lanes are everywhere, and wherever I went, I got the sense that all other means of conveyance deferred to the bicycles. Of course, that could be because it was obvious I hadn't been on a bicycle for 10 years and people were just keeping a safe distance from me.
If bicycles aren't your thing, walking is a good option, too. The city is compact, and everywhere you go it seems there's a good view. Trams are useful if you're tired, or cold, or in a hurry. They are comfortable, quiet, and seem to cover the city pretty well. They were also my arch-nemesis while on a bicycle, though.
You can also get taxis if you need to. And sometimes you do need to. It's better if you can avoid these, I think. I spent 10 euros on a taxi ride that I could have biked in about 5 minutes. There are plenty of one-way streets and streets along canals that just cannot be driven quickly. This may be the least car-friendly city I have ever seen, which was just fine by me.