Hotel in Amsterdam

What I've done is look in Rick's book.

Check out the Doubletree Hotel near Centraal Station. Another option is the Avenue Hotel which is a bit closer to Dam Square; there is a tram stop across the street. In the Jordaan neighborhood look into the Bank Hotel, and the Renaissance.

I hope you mean Sept 2020. Otherwise you're starting late. Amsterdam is extremely popular.

We stayed for 3 days in June at the Kimpton De Witt for under $300 per night though the rate depended on the day of the week. Thurs cheapest, Sat most expensive. It's about a quarter mile from the Central Train station. About as close as you can get to the action though surprisingly quiet at night. Quirky hotel, good service.

Try the Hotel Clemens, it is right on the transportation right on the street and right down from the Anne Frank House. We stayed there four nights, averaged about € 175 per night. Excellent breakfast.

If the hotels, don't pan out, try air bnb or VRBO
VRBO offers plenty of options including houseboats under $300/night

I have booked a houseboat in the jordaan district through airbnb. Under $250/night.
I was there 40 years ago and stayed in the youth hostel in the red light district. I’m too old for that now and dont think you should stay in that area. When i visited the anne frank house, i knew that was the neighborhood i would want to stay if i ever returned.

If still available, consider The Rho Hotel adjacent to Dam Square. The location cannot be beat, and breakfast is included in the price. I've stayed there 3 times in the last 7 years, and never disappointed. Great food in that area too. You might try Rene's for croissants or Golden Chopsticks for Chinese. Both a 10 minute walk.

https://www.rhohotel.com/en/
https://vimeo.com/350540797
https://renescroissanterie.nl/
http://www.goldenchopsticks.nl/en/

See what you think about the Owl Hotel. It is in a pleasant residential area and walking distance to the two major museums.

My first trip, using Ricks books in fact, I took his advice to consider Haarlem, it is about a 20 minute train ride away, but unless you are planning to party into the wee hours it really is not a bad commute. Over a half dozen visits since, I have always looked in Amsterdam, but as others mentioned, demand, especially on the weekends, is crazy year round. I also prefer not to set my budget up to $300, prefer less than $200, so in the end I have wound up staying in Haarlem each time, able to get rooms at reasonable prices even on short notice.

Haarlem itself is quite a nice town in it's own right, has a pretty active nightlife, a microbrewery, but much more laid back than the crowds of Amsterdam.

I would highly recommend the Dikker & Thijs Hotel , Prinsengracht 444, Amsterdam City Center which is in a wonderful location on the Prinsengracht Canal. It is within easy walking distance of the Van Gogh Museum, Rijksmuseum, Anne Frank House, and the Singel Canal Flower market. There is a tram stop right near it. Check Trip Advisor to see if they still have rooms. We used Booking.com and really enjoyed it. We chose a room with a canal view which was nice. Other rooms are less. They have a restaurant and a breakfast room also.