The lake district is about 500 miles south of Santiago and well worth a visit. You can take a long distance bus or a train as far as Temuco. If you want to rent a car then a gas guzzling 4x4 is necessary for that terrain so rent it locally to save on fuel and toll charges.
An hour's drive, or bus ride, west of Santiago are Valparaiso and Viña del Mar. The former is th main port of Chile and the latter is the main beach resort. There are two character hotels in Viña, the o'Higgins and the Cap Ducal. The o'Higgins was the grand hotel but has since been overtaken by the new Casino and Sheraton. The Cap Ducal is a gem from the 1930's in the shape of a boat overhanging the sea wall and boasts the most romantic seafood restaurant on the planet.
A good hotel in downtown Santiago is the San Francisco Plaza which is also home to the phenomenal Bristol restaurant. If the smog of downtown puts you off, the Manquehue in Las Condes is good choice but not for public transport.
http://www.delincatravel.cl/capducal.htm
http://www.chipsites.com/public/
For info only, don't use these people as they are unreliable,
http://www.gochile.cl/Home/Default.asp