Its mostly about a few things:
- offset
- the tyres you select (low profile is best, larger profiles will much more likely bang and hit the inner guards etc)
- Springs and how low/stuff your suspension is.
- Adjustable panhard rod or not
The diameter is not such an issue if the rear axle is centered properly with an adjustable panhard rod.
Even 14 inch rims that are wide enough are going to rub.
For performance you want to keep everything smaller and lighter. 15" is a great compromise that I've found to work best from all the wheel/tyre combos I've tried. I've had 13s, 14s, 15s, 16s. The 16s were too big and too heavy, the 13s give you too large of a sidewall - 14s are pretty similar, but better and still quite reasonable, and the cheap 14s I had were very heavy. 15s give you excellent selection of tyre choice, and you have a few options to play with. Overall diameter with 195/45/15s is excellent, or you can go fatter (i.e. 50 profile) to access a whole better range of tyres for cheaper prices.
If you're just after looks, then sure you will be able to fit 16s or 17s. Go for the lowest profile tyre, make sure you have an adjustable panhard rod. Stiffer springs may also help. Don't get a crazy offset. 16s I have proven to work fine. 17s I haven't done myself, but I think people have and if you consider all the above factors, it should be ok. Just compare the overall wheel/tyre diameter to that of a 16s setup using the miata.net wheel/tyre diameter calculator:
http://www.miata.net/garage/tirecalc.html