In general you don't want to leave unused inputs floating in either analog or digital circuits. It's inviting unintended things to happen. In the case of an opamp, the floating inputs will be very susceptible to noise and the output may flail around and even oscillate. This will not only put noise into the other circuits, but will consume power. For the same reason, don't tie the inputs together. Tie one high through a large resistor and the other low through a large resistor. That will put the opamp into a known and static state. Depending on the details of the opamp, you might get slightly lower power by switching which input you take where. Measure and see.