Providence to Burlington is a minimum 5 hour drive. As much as I think Burlington is a wonderful place (I live here, after all), I think you'll spend a massive chunk of your 36 hours just driving to/from.

Portland isn't quite as far, 2.5 to 3 hours (if you avoid driving in Boston's rush hour traffic).

Cape Cod is a much more viable choice given your very short window of time. You also ought to consider Newport RI as an alternative out of Providence.

In that short time frame, why spend so much time in the car? RI itself, though small, is scenic with lots of beaches and historic areas. Newport, like the previous poster said, is a fun destination, and it's only a 1/2 from Providence. Or how about Portsmouth, NH? We just spent this past weekend there, it's very scenic with lots to do. It really depends on what type of scenery and activities you want as well.....