You can pull the dash, get to the climate control stuff, pull off the larger box type cases and expose the heater core. You'll disconnect the two pipes at the firewall from the engine bay side. You'll then pull the heater core out into the interior. Plug your firewall holes with something, anything, don't leave them open. Connect the two heater core hoses to each other probably with a single hose. You can delete the in-hose valve if your car uses one to control heat. Put all else back together. Purge your radiator of air bubbles ("burping the coolant") and you should have successfully bypassed the heater core.
I suggest repairing it or replacing it. Having a working heater and functional defrost (for like driving in the rain and on cold mornings and nights) are important features for a daily driver. Even races cars (example: the SCCA improved touring groups) aren't allowed to remove their defrost/ heater setups. It's for function and safety. Removal of AC is allowed. AC is a luxury.
You can do it with the FSM or just get some tools and work your way through my summary.
All FSM chapters:
http://www.nicoclub.com/FSM/300zx/1986/
Heater Chapter:
http://www.nicoclub.com/service-manual? ... zx/1986/ha