Highly recommend looking in the Jordaan district for lodging. The deeper you go into the district the more real Amsterdam can be experienced.
Family restaurants, quaint shops, very very nice people.
The red light district is now mostly a tourist destination, but their are a lot of historic things to see and experience.
Definitely seek out some of the hidden churches, the Jewish District, and pull up at a outdoor restaurant/bar and watch the city go by...

Please do not leave Amsterdam with the Red Light district the most memorable experience. The city is SOOOOOO much more.