With the stock wheels, you can easily go 255/75R17s, which was the stock tire size on the JK Sport S. Some have gone to 275/70R17 tires, you gain some width but no real height. (The 255s are 32" tall, the 275/70R17 tires are 32.2" tall).
I have gone with 285/70R17 tires, but not on stock wheels. Stock wheels for the JL generally have 6" of backspace but some have 6.2" BS. Backspace is a measurement from the mounting surface of the wheel to the inside edge of the wheel. It determines how close the inside of the tire will be to suspension parts. Some have successfully installed 285/70R17 tires on stock wheels by adjusting the stops on the axle which determines the maximum angle the front wheels will turn. But, that also increases the turning radius of the Jeep.
I went with new wheels. I wanted the wheels because of the look, going with the retro styling of the Chief (a special edition based on the Sahara trim line), they also have slightly less backspace (5.2") which means I did not have to adjust my stops. I have no lift. If I was going off road in an area that required a lot of axle articulation, I would probably have gone with a modest lift (1/2" or 1" pucks would do it and are inexpensive, as you are using the stock springs and suspension setup.