I own a 1987 Corvette which has a poor idle and is sometimes hard to start. This car has 25,000 miles on it. I pulled out the spark plugs, and found they had black soot on them.
The "black soot" would generally indicate a "rich condition". "Rich" means there is an excessive amount of fuel in the air/fuel mixture entering the engine. Remember, it requires a richer mixture to run a cold engine. So if you pulled out that spark plug after running the engine for a short period of time while cold, that may normally give you a black sooty plug. But we'll assume that the engine was running at normal operating temperature when last shut down before removing the spark plug, indicating an abnormally rich air/fuel mixture.
The engine we're talking about in your Corvette is what GM calls a Tuned Port 5.7-liter V8. Tuned Port is just a fancy name for this particular port fuel injection setup, and port fuel injection simply means there is a fuel injector at each intake port for each cylinder.
There are many possible causes of a rich condition on this type system. A hard failure of most electronic components will store a "trouble code" while illuminating the Service Engine Soon light on your instrument panel. You didn't mention a light so we'll take these components off the list for now.
You might want to have this one checked out by a technician. I can tell you that the most likely cause of your problem is something which is a common drawback to the early Tuned Port design, and that is the fuel injectors themselves causing rich, hard-starting, and rough idle conditions. The injectors tend to contaminate easily, causing improper fuel spray patterns while losing their ability to hold back fuel pressure, and thereby causing symptoms very similar to what you have described. The new upgraded injectors hold up much better than the originals.