what is your citizenship?
How much it costs for the reciprocity fee depends upon one's citizenship. U.S. residents now pay $131 for the fee which is good for the life of the passport. Other countries have varying fees including as I recall from 18 months ago, UK and Australia. Other countries have no such fee, but may require a visa.
BTW: welcome to FT.
If you are from the U.S., the $131 fee applies even for a 10 minute visit. The airport is a fair distance from downtown Santiago, but the city is definitely worth visiting depending upon your arrival and departure times. I cannot comment on the lounge as the only ones that I have used are Lan's and Delta's. In September, we have 2 approximately 12 hour connections in SCL thanks to Lan's changing schedules and reducing flights. We will go into the city on both occasions despite having free lounge access.