Hi Matilda
How long have you got?! Wine regions in Chile now stretch from near La Serena in the North on the edge of the Atacama desert - a short flight from Santiago - way down south to the areas of Bio Bio and beyond towards the Lake District.
Decisions you will need to make is whether you plan to do tours yourself or go with guided tours - Chile has been slowly gearing itself up for wine tourism over the past 5 - 8 years - only this week I read news of a very interesting
new website where you can reserve tours, see who has winery restaurants (a real new thing there) etc.
Closest to Santiago, the traditional Maipo Valley has wineries you can tour on day trips such as Concha y Toro, Santa Rita or many others.
Also possible in a day trip but an overnight might be better is the Casablanca and San Antonio Valleys between Santiago and the Coast - here you will find Matetitc, Veramonte and others.
Perhaps the valley most geared up to tourism for longest - but mainly for group trips - is the beautiful Colchagua Valley around 150 miles south of Santiago with the little town of Santa Cruz as its middle - here you will find Montes, Casa Lapostolle, Viu Manent and many more - it has sometimes been dubbed the "Napa Valley of Chile" but be assured it hasn't got any of the Napa/Disney feel (apologies if this upsets anyone!) - or at least hadn't last time I went which was - I realize with horror - 5 years ago.
Hope this kicks off the planning for you. You might like to invest in a relatively recent book on Chilean wines - published in the UK, I'd recommend Peter Richards "The Wines of Chile" from the Mitchell Beazly Classic Wine Library (possibly different imprints out of UK).