I am assuming you'd like Metro access. But, I don't know if it goes to RFK stadium.

In any case, I did some searches and you are right, it is tough to find anything under $200 for that time period.

I did find one Marriot property that was around $170, but they're just over a mile from the nearest Metro station( and about 10 miles from RFK Stadium), which probably means a taxi from the hotel to the station, sorry.