I was in Amsterdam end of June 2016 for a week with my 13yo daughter. I did not go to Anne Frank and did not miss it. I did go to the Rijks at 9a when they open and there was no line. I bought my Museumkaart there. I also went to the Van Gogh. I bought a ticket for opening, and there was already a line. I loved both museums. I did not get a guide for either (audio or other) and felt the information provided (placards) was plenty. The Rijks is huge and I could spend 2-3 visits (as I can only stand to immerse myself in museums for about 2 hours before I glaze over), whereas in 2 hours at Van Gogh I saw everything and felt very informed and satiated.
I highly recommend The Old Church in the Attic! Its in the center of town, which I otherwise avoided (stayed mostly in the outer rings). We also went to the FOAM photography museum, and enjoyed that a lot.
I also highly recommend biking. Im not sure why people ask about the trams. We rented bikes for the week, and kept them locked outside our rental apartment, and biked everywhere. You can cover the whole city in 10-15 minutes, and its a thrill, and you feel utterly immersed in the culture of the city. It can be stressful, but remember, bikes have the right of way before people and cars. You just have to be consistent. My 13yo did great. Truly the most unique and fun thing about Amsterdam, and the Netherlands for that matter is the biking! If only everywhere had that infrastructure.
One afternoon we spontaneously decided to ride out along the Amstel river (because I recalled reading about that in RS' guidebook). We started at 4p without a map, just following the canal, along which there is a continuous bike trail, and within 10 minutes we were surrounded by cows, a windmill, and rowers in skulls on the Amstel. It started pouring rain (remember the rains of 2016, when the Louve flooded) and we got soaked through as we rode back into the city. Everyone else was out on their bikes too, commuting here and there like the rain was nothing, which it wasn't. We dried off at our apartment quickly, and headed out to a Rijstaffel restaurant in the Leidseplein. Great day.
I also recommend the Foodhallen for a lunch or dinner. The food is amazing, and on weekend nights they have ping pong tables.
People get so hung up on Anne Frank. There are so many interesting things to do that, unless you can get quick entrance, I wouldn't budget time for the line.