Sure. My wife and I spent a very fun evening on our last trip just riding the Monorail and boats around to many different resorts and exploring. We walked around the Contemporary and Poly, and later took the boat at sunset from DTD to several resorts just for fun.
I believe the monorail is open to the public, even if you aren't staying on Disney property you could technically ride it.
We were staying at a moderate and rode the monorail from MK to our ADR at California Grill
Yup, the monorail is free to ride as is all Disney transportation. When the kids were little, we would make the resort loop and head over to Epcot and back. They enjoyed it more than some of the rides in the parks.