Hi everyone, thanks alot for your anwers!
I had looked around at a lot of other threads, but just didnt seem to find anything that exactly asked my questions. Still looking around and searching in a lot of older threads, so please dont be mad for repeated questions; I am sorry about that.

Regarding a smaller city: I want to be in Santiago, to get contacts especially to the tech startup scene. I have heard alot about it, and compared to Lima it can only get better. I have been travelling in Chile before (6 weeks roundtrip of southering Chile & easter island) a few years ago, and last year I spend 4 days in Santiago meeting up with some friends and business contacts.
I would not mind living in a "cheaper" area - a thing about Santiago that I loved visiting it, was that the public transport system actually seems to work - although ofcourse more expensive than here in Lima. However it is unbearable to take public transportation in Lima every day, which also makes it very much more limited on where you can find a place to live. Most of the "middle-class" / "lower-class" places here in Lima are terrible (sorry to Peruvians) and extremely difficult to find affordable places for 1 person only (most people I know not living with a family, lives with at least 1 or 2 other roomates, because the only decent / nice apartments at the right price is 2 or 3 bedrooms).
Enough about Lima - I believe it will be a challenge to live on a budget that tight in Santiago, but it seems like (from several of comments from here and other people I have been in contact with from Santiago) that it is indeed possible. So I will hopefully jump on a plane within the next 3-4 weeks and take my chances in Santiago. I am already in contact with several possible apartments.
One of the problems I read about, is renting as a foreigner (without working visa etc). How much of a problem with this give me?
It seems like the best apartment options ask me to provide RUT (DNI for Chile right?), statements from employer etc.? Is there some way around this, when I just show up with my passport? Another problem is that I am self-funded for the moment, and therefore I cannot show papers from an employer (the main work I do is through my Danish company at the moment).. Anyone has experience in just coming to Santiago on a Tourist visa, and facing these problems?
Thank you all for your time.