At zero, there is "couch-surfing". Around 30 Euro will net you a bed in one of AMS's excellent youth hostels. Hotwire has a 4* at $88 for one date next April. You could bid on Priceline at the different star levels. And I've heard people describe under $200 as "cheap".
The couple of times I have been in Amsterdam, I have always had really good luck bidding on priceline. I suggest you go over to the Tripadvisor.com forum on Amsterdam. They have a thread that's been going on literally for years detailing all the bids for 4 star hotels. It's a great source of information and they are very helpful in that forum in how to use Priceline to get a good price for your stay. The thread you would be looking for is labeled:
hiusa.org will link you Hosteling International. Then click on "International". No age max. I stayed in one when I was close to 60. (There is a max in Bavaria, but that is the only place of which I know.)
As you have time, I would seriously consider finding some way of getting enough points to pay for a hotel, through credit cards or other promotions.
Hotels in central Amsterdam tend to be rather expensive.
It's not so bad at the airport, but then you may need a shuttle bus and train to get into the city, which eats up your short amount of time there.
easyhotel.com would probably work, and laterooms.com also have some smaller hotels.
Personally, after travelling that distance, I would want something better.
Just a good location is my main concern as I will be walking to most things.
In your first mssage you prefer the airport and now this? Thse two are not combinable. Stay in central Amsterdam and you can walk everywhere. Stay at the airport and you need to spend the 20 minutes in train/direction + short waiting time + 4€/direction + time to get from hotel to AMS. Not a god idea IMO.
I´s use Priceline or Hotwire. Most likely to get a good room within your budget.
Programs: NW Plat (now they call it DL Diamond) 1MM, soon to be DL Plat, Hilton Diamond, SPG Gold, Dusit Gold
When I overnight at AMS, I have always successfully booked via "name your own price" the NH Schipol for around $75 US per night + tax and fees. Negatives about this is that there is little in the way of food nearby. Perhaps the most expensive McDonalds in Europe across the street will please you. Plus the last time, they started charging 5 Euro for the return trip to the airport.
You might also check www.lastminutetravel.com which sometimes, but not always has astonishing rates in various cities. This is an opaque site, but with a little effort, you can determine with high probability where you will end up. Using a combination of of Expedia and LMT maps and amenity symbols will sometimes yield enough information to pin down the hotel. In the case of AMS, looking at the photos and matching them to Trip Advisor's will tell you for sure where you will be staying. Some photos actually give you a big hint such as the photo of an airport shuttle parked in front of the hotel. On the side of one van is a very large sign stating "Radisson SAS". The van is also parked under a sign reading "Radisson" Obviously this is not the Hilton van parked in front of the Hilton. A picture of the restaurant sign coupled with a quick Google search will often tell one the name.