For 2000 and newer Neons, I think you can do an 18" wheel and be fine...MAYBE even a 19, but I am not too familiar with the new generation Neons.
For 1999 and older, I know of a few with 18s but they get rubbing unless they modify their wheel wells a bit. I have 17's on mine, they are big enough for the car in my opinion. I do get slight rubbing if I am making a right turn and lock the wheel all the way to the right.
Here's my beast with 17's
