Kangaroo Island is an island off the coast of Adelaide. A short drive to Cape Jervis and ferry trip will put you at Penneshaw in K.I. If you don't have access to a car Sealink provides buses that will get you down to Cape Jervis. Their website (http://www.sealink.com.au/) will also provide ticket prices, accommodation spots and tours and packages.
There is some beautiful scenery and wildlife to see, particularly the seals and sunsets on the beach. There is also the opportunity to see baby kangaroos and hold them as well as koalas. A lavneder farm has lovely tea and cakes and there are some lovely gifts for friends and family.
Winter might not be the best time to enjoy the sea but the accommodation caters for all seasons. Worth a visit at least once during your student/working career in Adelaide! =)