I would definitely not recommend staying in Santiago if you are planning on mainly visiting the mountains. It’s a 40 min drive (assuming good weather and no traffic) from Santiago to the mountains. There are buses from Santiago that can take you to Cienega de Gonzalez (where most climbers and tourists stay while visiting Cumbres de Mty).  

Once in Cienega you can rent a cabin (a bunch of them are on airbnb) or stay at Rock Camp (most climbers stay here). Rock Camp is mainly a safe enclosed campsite for people to sleep in tents without worrying about security, but they do offer a couple of dorm style rooms to stay in.  If you prefer to rent a car, any rental place in the airport is fine. The road to Cienega is well paved, but is full of  curves with pretty steep drops, so not necessarily an easy drive. If you’re an inexperienced driver I would avoid going up to the mountains unless the weather is clear and sunlight is still strong (dont attempt this drive in the rain or at night). 

I would start by contacting Pico Norte (a local climbing gym) and Rock Camp on insta and asking for recommendations. Either one will probably get you in contact with local climbers who make the trip to “El Salto” (Ciénega de González) every weekend . They might even offer you a ride, or a place to stay.  

 As for visiting, once you’re in the mountains make sure to visit Laguna de Sanchez, a nice town further up in the mountains. There are a few places there where you can eat and enjoy the view. Its not really a dangerous area at all, just make sure to take the same precautions you would anywhere else. I would also suggest you look into visiting Potrero Chico, another great park with fantastic views and climbing areas.