The basement drain slopes in, as it should I suppose for drainage. It is right where you walk into the bathroom. Is there some sort of false flooring I can put over it or a large drain grate over it?

What you could do is recess the floor enough to accept a grate installed at floor level. Check them out at: http://www.plumbingspecialties.com/downloads/Grates&Drains.pdf
Good luck, tom