Tires and Wheels
Replacing the tires and wheels on a stock Corvette immediately makes your Corvette stand out. It is probably the easiest way to modify the appearance without extensive fiberglass work and without the risk of ruining your car. If you don’t like the rims you can always put the stock ones back on and sell your aftermarket rims. Additionally, if you’re careful about which wheels you select you may also decrease the unsprung weight of your car which will help your car’s handling.
Increasing rim size can help make turn-in a bit quicker and handling even sharper (because there is less sidewall flex). While most people change their car’s rims simply for aesthetic you can also improve performance. Similarly, by getting wider tires (and wheels) you increase the size of the tires contact patch and thus increase your grip.
What are the negatives? Well, an increase in tire width will increase rolling resistance (meaning increased fuel consumption). Increasing wheel diameter (going +1 or +2) will give you a harsher ride (and you might crack a rim over a pot-hole) because there is less sidewall to flex. And if the rims are heavier than the OEM rims your braking and handling will suffer due to greater unsprung weight.
One thing to note however is that the C6 had a Tire Pressure Management System (TPMS) which may, from time to time, need to be reset or replaced. This link is a great place to start.
Want some inspiration? Check out this gallery.