Right, with Amsterdam it’s very important to know where you go. Basically look at it like this. Anybody visiting Amsterdam will, usually, start of at the Central Station. (There are something like 10-15 trains per hour between the airport and the Central Station, and be aware – taxis are EXTREMELY expensive in The Netherlands! So almost everyone goes by train.)
From the Central Station, you look towards the south-east. Right in the middle in front of you is the Damrak, the long, major street towards Dam square (after that Damrak turns into Rokin). Basically, you can follow the Damrak, and go anywhere to the right – but better avoid anything to the left (ie, northeast) of the Damrak / Dam / Rokin line. It’s pretty easy to see what I mean on Google Maps. The ‘safe’ line goes around in a circle towards Waterlooplein (metro station) and the Rembrandt House Museum which you easily see on Google Maps. Basically, avoid everything within that area.
There are plenty of amazing places such as the markets (Waterlooplein, Albert Cuypstraat), the canals (just walking along the canals is really nice, especially in the evening), and just the general feeling of a (relatively) huge, very busy European classical city. It’s totally different from NYC, I think – not that I’ve ever been there. Amsterdam has a lot less cars in the city center, I suppose. The streets are much smaller. But the mix of all kinds of people (both inhabitants and tourists) generally living together in peace is amazing. And just the sounds of the city – even though I never lived in Amsterdam myself, I always particularly enjoy hearing the sound of the trams. It’s a happy sort of sound. Taking trams to tour the city can be nice also, for example Tram 5 which goes from the Central Station via the city center towards the Jewish area (Buitenveldert and the suburb of Amstelveen) is very nice.
Anyway, I’m off…