Cape Leeuwin is the southwesternmost tip of Australia, where the Indian Ocean meets the Southern Ocean. It’s one of the trio of Southern Hemisphere capes used as checkpoints in 'round-the-world sailing competitions, the others being the Good Hope at the southern tip of South America and Cape Horn at the southern tip of Africa.

The lighthouse at Leeuwin (Latitude 33° 22' S, Longitude 115° 08' E) is apparently quite a tourist attraction. Built in 1895 and manually operated until 1982, when a 1,000-watt halogen lamp was installed. The cape also houses a small memorial to ten sailors lost when the HMAS Nizam nearly capsized just off of Leeuwin in 1945.

The coastal area around Leeuwin is apparently good for surfing. The Leeuwin current is a thin (30 km wide) warm current that runs north to south, hugging the western Australian coast and sheltering it from the cold Southern Ocean current that runs north from Antarctica. The warm water, coming down from Indonesia, allows coral to grow there despite the low latitude.

Near as I can tell, the closest sizable town to Leeuwin is Augusta.

Sources:
-- http://www.memorials.eplugz.com/memorials/sthwgtsth/leeuwin/leeuwin.htm
-- enviroWA (Western Australia): http://www.cwr.uwa.edu.au/~ewing/envirowa/coastal/leeuwin/leeuwin.html
-- Lighthouse page (the URL looks funny but works on my Mac): http://www.lighthouse.net.au/lights/WA/Cape%20Leeuwin/Cape%20Leeuwin.htm
-- UWA Sports: http://www.sport.uwa.edu.au/~uuc/diving_wa/leeuwin.htm

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