Priceline is sure to have plenty of options under $100. Check out betterbidding.com for a list of successful recent bids.

It's also possible that Harvard might have a 24-hour library. Many universities (including my alma mater, the University of Virginia) now keep one of their libraries, or at least a dedicated study area, open all night.

You might also consider flying one-way up to Boston and then taking Amtrak's night train on your return (I believe it leaves at 10 p.m. and arrives in DC at 7 a.m. the next morning).