Snuff, the diameterof the wheel itself is not important, you need to focus on combination of offset and width.
First you have to understand what offset is.
The offset of a wheel is the distance from its hub mounting surface to the centerline of the wheel.
In our case, the hub mounting surface is positive (+32mm) toward the front or wheel side of the wheel. Positive offset wheels are generally found on front wheel drive cars and newer rear drive cars.
If you increase the offset, your wheels will sit further inwards going closer to the struts, but also will look skinner and not fill out the arches.
So generally speaking you want a wheel with a lower offset than you currently have.
you can achieve this 3 ways, either:
1/ fit a wheel with a lower offset for example, from ET32 to say ET20 (more tricky as most wheels to fit S3s are ET35)
2/ using spacers - an ET32 wheel, with a 10mm spacer will give you a net ET22
3/ wider wheels
A 1" wider wheel with exactly the same offset will give you 12.5mm less inside clearance and 12.5mm more outside width or arch-fill
I just put a set of 18" on mine, but also went wider.
your stock wheels are 7.5" wide, with an offset of ET32
I have just gone up to 8.5" wide fronts with ET35, but also installed 5mm spacers. the fit is extremely tight on the inside (due to large rim protectors on the tyres), but doable
i went 9.5" on the rears and fit was no problems whatsoever (note I had to instal 5mm specers to ensure that the deep dish rims cleared the brake caliper - called 'x-factor')
(and I'm running Koni coilovers)
On a seperate note, and as mentioned, you need to focus on 5x100, which is the stud pattern - you can get 5x112, (which will give you a great range of wheels to choose from), but you will need to purchase adapters which is more cost