May I have a suggestion of a hostel or inexpensive hotel close to the Ann Frank House?
We stayed at Vondelpark hostel. It's really closer to the Rijks and Van Gogh museums but it's not hard to get to the Ann Frank house from there.
The hostel is reasonably clean and cheap. It has a no drugs policy but you have to walk through a crowd on the street smoking pot to get to the entrance.
We stayed at the t'Hotel about a block away from the Anne Frank house on Leliegracht. It wasn't cheap, but not much in Amsterdam is.
We stayed at Vondelpark Stayokay too, and it was fine. Good ,large breakfast and close enough to walk to Anne Frank House.
Hotel Brian
Singel 69
Honestly the above name and address is true. Cheap, very basic and a lot of fun.
It's ten minutes walk from Anne Frank's house.
I haven't used Brian for many years but it was a haven for me in the days when cash was really tight. It's located very central and in a safe area but there is a small red light street behind the hotel. This is normal for Amsterdam Centrum and it's very safe indeed - you won't be bothered.
The Chic and Basic on the Harengracht is in one of the best locations in Amsterdam. It's fairly reasonable, by Amsterdam standards.We rented a room for a week for friends, while staying across the canal. They enjoyed their canal view room, but it did have some killer stairs. You can walk to everything from here. Anne Frank House is about 7 minutes.
Google the Hotel Van Onna. They have an annex that should be fairly reasonable.
It's been about 5 years, but I liked the Shelter Jordaan. Clean, reasonably quiet, and convenient. I was a little concerned about it being a "Christian youth hostel" but didn't find that so scary in practice... it basically kept the hard-partying elements out of the place, and in Amsterdam, that's a good thing.