Need a little help here please.

Where does the thick wire coming out of this alternator SUPPOSED to go to in our 1964 273 ?

It's supposed to go to one of the bulkhead terminals and from there to a splice before the ammeter. The splice goes to the ignition switch, headlight switch and part of the fuse box. It's the same way on the 65, except instead of using terminals, the 65 uses solid buss bars to conduct the electricity from the battery, through the ammeter and out to the alternator (your black wire).