One way to make it "big enough" is to put a weight on the end of a long cable, and spin the combination. It wouldn't need to be a full g either, some should be a lot better than nothing.
With a cable, though, there might be weird problems with oscillations.
One alternative is to replace the cable with a rigid tube, and then have living quarters at both ends. The tube is big enough for an astronaut to pass through. Sort of a one spoke section of a spoked wheel.
With a cable, though, there might be weird problems with oscillations.