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There is no fixed points in space. The sun is the best frame of reference for Earth though.

This is pretty much it. (Rest of comment is more directed at the rest of the conversation than you Bogey)

Any motion at all is always in relation to a certain point that you have to define. You may be sitting still in your living room, but you're actually moving at a thousand-ish miles per hour, just based of earth's rotation. But let's say if the Earth is defined as your fixed point, then yes, the Sun does 'revolve' around the earth. All the other planets 'revolve' around the Earth, with the Sun as the center or their respective orbits. Relative to Earth, you would get a slightly loopy, off-centered orbit.

Also, you can't really consider the Sun to be a fixed point either, as it is revolving around the center of the Milky Way, which is itself moving through space. And within the universe, how do you determine a fixed point that defines all motion universally? Where, exactly, in space can you set your 0,0,0 that gives you a definable movement for any given object?