At SCL, stay airside—long immigration lines and distance make lounges and dining the better choice.
A 3-6 hour layover in Santiago is possible but tight. The Centropuerto bus ($20) takes 45 minutes to the city center - factor in 90 minutes back. You will have about 1-2 hours in the city. Focus on one neighborhood: Lastarria or Bellavista for cafes and street art. A cortado and an empanada are the priorities. Leave 90 minutes before your flight for the return bus.
Six to ten hours is the sweet spot for Santiago. Take the Metro from the airport (Line 2, 45 min, $1.50) to Baquedano station. Walk to Bellavista: explore the street art, visit the Pablo Neruda Museum La Chascona (45 min, book online), and have lunch at one of the restaurants on Pio Nono street. Cross the Mapocho River to Lastarria for coffee and bookshops. On a clear day, the Andes views from elevated streets are spectacular. For dinner: Chilean empanadas, chorrillana (fries with beef and onion), or fresh ceviche. Return via Metro - allow 75 minutes.
With 10+ hours, add Cerro San Cristobal to your itinerary. The funicular from Barrio Bellavista runs to the summit (900m altitude) for panoramic views of Santiago and the Andes. On clear winter days, you can see Aconcagua. Mercado Central near the river has an outstanding seafood hall - arrive for lunch, order the caldillo de congrio or locos a la mayonesa. The Museo Chileno de Arte Precolombino near Plaza de Armas is small but excellent for pre-Columbian gold and textiles. The Vitacura neighborhood (20 min by Metro) has high-end design shops and good restaurants if you want a contrast.