The best mileage classic car is one that is properly maintained. This includes taking into account the overall condition and mileage of the car. Any car with a few miles on it needs to be properly tuned by a mechanic that uses "the book" as a starting point. A rebuilt car is exactly that and should be adjusted to as new only as a starting point. If you have new carb(s) or rebuilt carbs, then take this into account with the final adjustments including how they need to work with the rest of the engine. The same with the point gap on the distributor, use the recommended settings as a starting point. I don't even closely recall how many properly tuned classic car engines I was able to get running better, and hence getting better mileage, with only a few simple by the ear adjustments, that take into account the full condition of the engine.
Apart from getting the engine tuned by a pro to take into account any wear on any engine components, you need to also make sure everything else is in proper condition to not only make the car run correctly but also drive for enjoyment. If your classic car has properly inflated and the correct, per the condition of the rest of the car, and you also need to make sure all associated components are correct. This means getting all suspension components to be in top condition.
If your car is not a fully restored concours example, then maybe upgrade to any of the many upgraded performance components for many classic cars.
The best mileage classic car is the one that is in the best condition it can be in, taking into account the mileage and overall state of the car and all of its components!
The best mileage is from not only your choice of classic car, yes some will get better mileage than others, an MG midget should get better mileage than a dino 246, but, in the end, it will be the properly tuned, adjusted, and maintained (right down to air pressure in the tires) classic car that gets the best mileage! Choose your classic car based on what you want for looks and performance, then find a good mechanic that knows your car, and can get it in the best shape possible.