We would recommend spending a couple of days of your holiday exploring Santiago itself and while you're there, make sure you head up San Cristobal hill with your camera, to get the best views of the city and the surrounding Andes. After this, move on to its surrounding attractions; the coast, Andes and vineyards.
The food in Santiago is great; from the bustling central fish market to any number of upmarket international restaurants and more typical Chilean lunch options. South of the city, the Central Valley is where the majority of Chile's wine comes from. The Maipo Valley, closest to Santiago, is home to the most widely known export; Concha y Toro, whose winery can be visited in a day trip. Maipo's cool ocean breezes, bright sunshine and elevated slopes are perfect for Cabernet Sauvignon grapes, one of the export varieties Chile has become synonymous with, but local vineyards also grow Merlot and Chardonnay on the upper slopes.
Beyond that, deeper into the picturesque landscape of vines with the Andean backdrop, are many smaller vineyards, some of which form part of the 'Wine Route' and offer charming overnight accommodation. Try a glass of delicious Carménère red wine - the grape was originally from the Bordeaux region of France but is now almost exclusively grown in Chile.