Is it a good idea to change a 1973 cad. from havoline 30 wt. oil to a full synthetic oil. I bought this car new. It has 66,000 original miles. Driven less than 300 miles/year. Stored inside.
The main advantage with synthetic oi is longer distance between oil changes. You only drive a few miles per year, and extending oil changes is a bad idea. Oil, even synthetic, takes on moisture from the air each time it cools down after driving, and allowing a car to sit unrun for a long time allows the moisture to affect the engine. At less than 500 miles per year, you should change the oil/filter at least every three years; more often if you're in a humid climate. Synthetic will have no advantage for you.
Stick with the 30wt. oil unless there are other problems you are trying to solve like difficult starting in cold weather. Then you may want to go with a multi viscosity oil like 10W-30 but stay with the regular oil rather than a full synthetic.