It starts and runs fine and then just dies going.

The biggest clue is how it acts when it dies. If it spits and sputters, and backfires, suspect the ignition pickup coil in the distributor. This happens most commonly to those with the vacuum advance unit on it. A valuable clue is it won't cut out if you unplug the vacuum hose and plug it. That failure is due to the flexing wires. Regardless if the vacuum advance is on the distributor or it's on the Engine Computer on the air cleaner housing, the pickup coil can fail from heat. In that case you won't have spark and the engine won't restart until the coil cools down, typically in an hour or more.

If you slowly loose speed and power over a period of as much as a minute or more before it stalls completely, suspect the pickup screen in the gas tank. The big clue is the engine will not restart for about five minutes, then you'll only make it half as far before it happens again. As soon as it stalls, remove the air cleaner cover, look down the carburetor and work the throttle by hand. If you don't see one or two nice streams of fuel, suspect that pickup sock.