I recently hooked up my battery backwards on my 1967 Datsun Fairlady SPL 311, saw some smoke come from the engine and now my car won't start. Any suggestions on what went wrong?

I want to say cars that old had fuseable links that blew when a battery got hooked up backwards.
You could try looking for their location with one of the old service manuals located here:
http://www.nicoclub.com/datsun-service-manuals

PS - welcome to NICO!

Worst case would be a fuse. Any idea what side / where the smoke came from?

You can also take a flash light and look through the engine compartment for any wiring that has melted plastic. You can also take a voltmeter and check the fuse box items (key on) to narrow it down.

When you turn the key, does the starter crank? What does it do (if anything).