What? Google hotel deals and as far as " how much money do they pass?" You can't carry more than $10,000
There are no cheap hotels anywhere near this airport (very expensive area). Maybe you could try Airbnb.
Go to tripbeat.com and search for affordable hotels that you can stay.
I don't know about budget hotels but Americana Hotel in Crystal City looks like a pretty low end one as it's not very well known and pretty small hotel. It's actually like 5 minutes from the airport. Note though the transportation is a bit trippy.
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