If you want to avoid the big commissions to dealers or the auction houses, you have to sell your car yourself. You can reach a large worldwide audience with an ebay auction, and ebay allows you to set reserve prices, end the auction early if you sell the car off-line, provide as many photos as you want, answer questions, and set the length of time for the auction. You can do all this for $100-$150 dollars. Many collectors have listed their cars on ebay with an absurdly high reserve price just to see what kind of bids their Corvette will draw. That's one way to get an objective appraisal!
Obviously the downside of selling your car at an online auction is that no one's there to pre-screen your buyers or act as a middleman to make sure the buyer's money is real. You need to be careful not to accept a counterfeit cashier's check or money order, and make sure that the buyer is not just a prankster who will disappear when the time comes to close the deal.
You can sell your car at low cost or for free using many of the online auto sales sites. Some of these may charge a fee, and their results may be mixed. In general, if an online site wants money to help sell your Corvette, make sure that you owe money only if and when the car actually sells.
The cheapest way to sell a car in the modern world is to use Craigslist. This is a free classified advertising site that has exploded in popularity in the last few years. Because Craigslist does not charge individuals for classified ads, allows photos, can keep your e-mail hidden, and allows people to search only for what they want, this website has decimated newspaper and local bargain sheet classified advertising in North America and around the world.
But if you guessed that there are trade-offs to using Craigslist, you're right. Craigslist acknowledges the dangers at the top of every screen, and has a dedicated page to teach you to avoid the scams and cheats that prey on the naïve and trusting. Mostly, the scammers will respond to your ad with some strange story about how they're out of the country right now, but want to send you a cashier's check and have you deliver the Corvette (and the title) to some third party. Be extremely suspicious of any strange transaction that doesn't involve cash and the kind of reasonable caution on the buyer's part that you would expect from someone laying out a large amount of money.