I booked two nights at the Nadia in early April just 36h before turning up - it was one of the last rooms available in such a central location, just off Dam Square and in the Western Canal cafe and shopping belt.
The hotel is in a building on Keizersgracht canal up some very steep stairs, but they'll bring all your bags up and down; and the rest of the time...I guess it makes up for the lack of a gym...and all those pancakes.
The other downsides are that the rooms are tiny and they can be strict on the no-visitors rule. They are cosy, spotless, warm and quiet though. Also, the attention to detail makes a difference: the fridge is great to stock up on drinks from the nearby Albert Heijn supermarket, and the kettle was good for a cuppa coming in from the unseasonable cold. The shower heads are cordoned off quite effectively from the rest of the mini bathroom so the floor might get wet, but little else will. For the record, water pressure and heat were excellent - even on the fourth floor in the primetime chilly morning rush.
Other perks included wireless internet and super management (welcome drinks, plasters for blisters, a toothbrush at midnight, taxi to the airport...you name it, it was taken care of with a smile).
Summary: I had called a million places and Nadia's rates on absolute terms are about as low as Amsterdam gets. You might be able to find a larger place if you try earlier, but Nadia is tough to beat for convenience, reliability, friendliness and last-minute availability.