From what frame of reference does the Earth orbit the sun?

With reference to the fixed stars in the background, the aggregate of which is stationary. Being at such humongous distances any movement of them is ironed out and we get a pretty dependable frame of reference, the best next to the hypothetical (theoretical) 'absolute' frame of reference which is theoretically (by its own definition) impossible. So hitch your wagon to that, you'll never go astray.