My count on chassis grease nipples is seven on each side of the front suspension (14), one on the drive shaft just behind the transmission (1), and two on the rear swing axle (2) for a total of seventeen. Some earlier cars may have another one the driveshaft center and the steering idler arm.
The early BBB has a nice diagram with photos of each location on page 0-9/1
Include in your lube service, the hood hinges, the engine linkages, and the ignition distributor. The door lock, trunk lock and ignition lock should be occasionally lubed with a graphite lock lubricant. While your at it, lube the grease point on each door hinge.
Early injection pumps have a self contained oil supply which also needs to be checked and changed occasionally.