You could play with
www.rome2rio, entering Boston as a start and then some reasonably nearby city as an end. Quincy, Salem, etc. The site will show various ways of travel, with train to my two examples both under $10. Then there will be a click option for accommodations.
Maybe you will get lucky and find some interesting nearby city with lower hotel rates?
And I'd think you might be able to do somewhat better than the hotel rates shown by rome2rio.
Romelle