I think the amount of times you can drive your exotic without looking way out of place depends on where you live.
I live in LA and there are plenty of places you can drive an exotic and be right at home, there are also plenty of places where i wouldn't drive a half decent car through.
If you are barely on the cusp of being able to afford an exotic then I don't think it's worth it. You would be too afraid of driving it for fear of something going wrong (and the ensuing financial strain that would place on you).
If you are at the level where you are "ok" with something catastrophic happening to your exotic then i think you would be more inclined to drive it often.