The gap will be the same whatever size wheels you choose to within a few mm, as the profile needs to be reduced as you increase the rim size (otherwise your speedo will be out). To reduce the gap, you'll need to lower it.
Do the sums, and you'll see that all of these common Golf tyre profiles are almost exactly the same total radius:
195/65/15
205/55/16
225/45/17
225/40/18
x/y/z where
x=tyre width in mm,
y=profile as % of width,
z=rim diameter in inches.