Hey, Alice. Do you have a place to stay in Santiago? Quite a few of the hotels have a draw in that they offer free parking, which is what my friend and I did. Other than that, it is metered all over the downtown and maybe someone can correct me, but there is no free parking in the old town at all. It'd be best to take public transport in, anyway, as the traffic is miserable in that area as the streets are very narrow.
The universities have recently installed metres, as well, eliminating them as a source of free parking. Boo :[ about 8 years ago
When I went to Santiago I stayed in a hotel called Miradoiro de Belvis http://www.booking.com/hotel/es/miradoiro-de-belvis.html
It had complementary parking which was very handy. Also the cost of the place was quite cheap considering it was in the middle of old town it was only €45 total a night for a double room. about 8 years ago