Hi Laurie,
I think I would park the car in Santiago and take the bus up to Ferrol, but I think you could do it either way. For me I think it would be good to have the car there once I finished, and not have to "travel" to pick it up, but either way I think it would work.
If you would like to park it in Santiago, the only long term parking that I know of is about 1-2KM from the airport. Have a look here:
http://www.aparcamientolavacolla.com/index2.asp
.. the airport is about 15 minutes by car outside town.
The alternative would be to park it in Santiago, in a regular underground parking. I would consider this safe, but it may be a bit pricy. I wish I remembered the prices, but I would guess about €20/day (pluss-minus some euros).
One good (24 hour) parking is this one.
In the city center all streets have meters, so leaving it there would not be an option. Even the university campus now have the meters, so leaving it there would not work either.
I hope this helps a bit.
Greetings from Santiago,
Ivar