To clarify a few things - my understanding is that the OP is travelling from Antofogasta to SCL for this stopover - so they will already have had to pay the reciprocity fee when they first arrived in the country. They will not have to pay it again for the day layover in SCL (the reciprocity fee covers you for multiple entries for 3 mths)
And expanding on Rooflyer's advice, that fee is paid when you get off the plane but BEFORE immigration - when you get off the plane you will have to walk down some steps towards immigration. DON'T immediately jump in the immigration queue which is immediately in front of you - instead make a hard left turn and you will find a few booths where you pay the fee - THEN jump in the immigration queue
For that return trip with the layover, can you clarify exactly what times you are doing? I understood that you arrive at midnight? And leave just after midnight the next day? (Which would be on the LAN metal flight?)
If you are flying in business, when you go to check in at SCL you should use LATAM's vip checkin - it is to the very far left of the main departures area, up a flight of stairs (or lift). It is not that easy to find if it is your first time. So remember, go into the departure checkin area, head WAY to the left, up the stairs, and along a narrow walkway until you find it. (There are one or two tiny shops /offices before you get there)
Using that vip checkin is very quick, and has a dedicated emigration booth and security which is fantastic and swift. This takes you into a foyer where you access the lounge, which you would be entitled to.
Great lounge, decent food, very good wine, etc. Has showers, internet, and even on the top floor (it has two floors) there is a little sleeping room with four beds. I have managed to kill many 12hr stopovers there without getting too bored. It has (also on the top floor) some great lounge seats with fantastic views of the airfield - in case you like watching planes
So definitely, if you dont feel like touring the city, you could survive there is necessary. (BTW to access the rest of the airside shops/restaurants/etc you go out of the lounge and will find a lift or stairs that take you down a floor to the main airside departures area. When you come back to the lounge it is not exactly well signed - very discreet - but it is there.
Last comment, regarding the luggage. I agree with Boca68 that I would not be entirely happy doing that, even if it is possible. Mainly because I distrust their ability to ensure it is not temporarily lost. I am sure the hotel would hold your luggage for you if you decide to do the city thing. If you want to do the lounge thing though, then I would try to do the check-all-the-way-through from Antofogasta - I have arrived very early for flights at SCL and even at the vip checkin they were very reluctant to checkin baggage many hours before flight. I won (hold excellent status with LATAM and QF) but I suspect I was lucky. In any case, you can try to checkin early, and if they refuse, you can go back to Plan B and leave it at the hotel and do a city tour.
I hope all this makes sense and is helpful
