I've been a couple of times and done the following: wine tastings at vineyards in the Maipo Valley (within 1.5 hours of SCL), toured Pablo Nerudo's homes in Santiago and Valparaiso, self-guided walking tour of Valparaiso (found some galleries with attractive artwork), and spent some time on the coast watching the waves. Did a fair amount of eating at local's restaurants (lots of good ceviche, abalone, and pisco sours). Enjoyed a fancier steak dinner at Happenings (in the el Bosque neighborhood). Hung out at the restaurant at the soaring club located at one of the small airstrips right in Santiago. Checked out the arts and crafts market at the end of one of the subway lines.
It's easy to get around Santiago using the subway. Taxis are an expensive way to go places. Renting a subcompact car is more expensive than in the US, but would be the way to go if you want to visit the wineries or go to the coast.