I would believe your flexibility would be best searching for hotels outside of the City of Alexandria and in the 'Alexandria' area of Fairfax County (just on the other side of the Beltway) - there are two Alexandria's! Search for hotels in the zip codes 22303; 22310 and Springfield, Virginia. They are close enough to Metro stations to get you to the King Street Station of our Metro.
I hope you find this helpful.
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