Hi, I lived in Amsterdam for 4 years so I can give you some tips.

1. The best period would be from now until September then it get cold again. Please note NL is never a particulary warm country and is also quite rainy therefore bringing an umbrella is important as bringing the money! 

2. Amsterdam is not a particularly huge city but the best areas to stay are the ones very central such: Rembrantplein, Leidseplein, around Dam square and along the canals. The Red Light District has been renovated and is not as it used to be (actually, unfortunately) but is still the "backpackerts area" of the city. Be aware of the fact that the hotel's standard is a bit below the average of other countries and rooms can be quite small. If you want I can give you few names from 2 to 5*

3. The best things to see are the Van Gogh Musuem and the Rijskmuseum. I'd avoid the Heineken one and the Scheepvart Museum because they have lost some charm after the renovation. I've never been to the Anna Frank's one but I've heard mixed reviews. The best thing to do for me remain to rent a bike and wander around. Also take a canal cruise is a nice way to see the city under a "different" prospective. You can also rent your own little boat. Amsterdam is a beautiful/romatic city: Joordan is a very enjoyable neighborhood, as well as take a stroll along the canals and Vondelpark.

To go out: tourists (but also locals) tends to go out in the Red Light District, Rembrantplein and Leidseplein. Otherwise grab some flyers around and check what's going on. If you like live jazz music  there's a typical cute place in Leidseplein. There's is the sign with a saxophone outside.

Ik wens je een uitstekende tijd in Amsterdam te hebben!