gum answered your questions admirably, as is her wont, so there’s not much to add.
The Den Tex-straat is located in a fairly quiet block of houses, which is quite near the centre. So I guess the description is correct.
Weather, as gum alluded to, is highly unpredictable. We may have heat waves (which means 20-30 degrees Celsius), but it may also be pouring rain for days on end. So have both light and warm clothing with you. One thing to remember is that in Amsterdam most rain only lasts for five minutes, so your best bet is to hide somewhere until it stops. The converse also holds: nice weather may suddenly change for the worse. Therefore don’t leave the hotel without a portable umbrella. Temperatures on the whole may therefore vary, I guess, from warm summer (30 Celsius at day, 20-25 at night), to chilly (10-15 Celsius at day, 5-10 at night). Normally it is somewhere in between. August normally has the best weather so is relatively dry, but don’t count on it.
I have heard some stories about pickpockets, so you may want to carry your stuff in a belt or other safe thingy.
What kind of sights do you like? The Maritime museum is apparently the quietest museum in the world. The Amsterdam history museum is nice if you like history. It explains a lot of aspects of the city, including the history of the red light district.
The Jordaan, as Pookey said, is a nice residential area to walk through. There is a farmers/biological market on saturday morning. The Filmmuseum and Vondelpark, as said, are really nice and show you the locals relaxing. The restaurant at the top of the Okura hotel apparently has a good view of the city, but I’ve never been there, and it may be pricey (but I’ve heard you could also just have a cup of coffee there).
There is a Hortus botanicus (botanical garden), but I think the one in Leiden is better (you can reach that by train, a journey of 30 minutes, plus 15 minutes walk). Leiden en Delft both have petite pretty city centres with canals and canal houses. Distances to other cities by train are fairly short: The Hague is 1 hour, Leiden is 30 minutes, Delft and Rotterdam a bit above 1 hour. Arnhem (which is where you have to go for Kroller Muller) is 1.5 hours. Maastricht is 2.5 hours, I think. With respect to Kroller Muller: you can (I think) buy a combined ticket at the Amsterdam station, which gives you train journey, bus travel and entrance ticket in one go.
If you are interested in getting to know Dutch local culture, you should visit cafe’s. That’s where most Dutchies hang out. You can eat in ‘eetcafe’s’ (eating pubs), which serve a simple fries-meat-salad meal for roughly 10 Euro. Later at night you can continue drinking there (or at other cafe’s). Or you could go out: the city has a great night life (which unfortunately I’m not too well informed about these days). You can go to Paradiso (a former church turned pop concert hall), the Melkweg (rock concerts but also movies). Recommended is also to see a movie in Tuschinski: a gorgeous art deco style movie theatre. There are several jazz cafe’s, hip disco’s and clubs. Avoid the Leidseplein (tourist trap), see the Rembrandtsplein (where the cool kids seem to hang out), or go to the Nieuwmarkt (where there’s lots of cool cafe’s). The better cafe’s for locals are not in those places; you may ask the person you’re meeting about those.
Amsterdam is indeed mostly casual; we’re used to so many weirdo’s that we don’t blink at seeing another ;). However, the one rule to remember is that we don’t like people being troublesome. If you ask politely, most Amsterdammers are very open, but if you’re rude or demanding, you may meet resistance. But you sound as if you know that already.
Dress code is quite liberal, but the easiest way to go is to have relatively plain, subtle clothes (monochrome, small markings). More outspoken colors may make you stand out in places even when you wouldn’t want to.
With respect to monetary matters: credit cards are still not as widely used as in the U.S. You mostly only use those for restaurant and hotel bills, or expensive stuff. Usually people pay with cash money or with debit cards (‘pinnen’, we call it).
If people are interested in a little get-together, I might be up to it. I’ll watch the thread; you can e-mail me if you like. We could taunt gum (I hope it’s not something bad keeping you from leaving home). However, I’m not really up to date on Amsterdam night life.