Prickly Pear Stays Plympton is in the inner southwest of Adelaide. It is the quintessential leafy suburb in Adelaide, perfectly located 10 minutes from the airport, CBD and Glenelg Beach. The Anzac Highway runs through Plympton going from the bay to the city, with public transport at your doorstep. Think of Plympton as the gateway suburb for Adelaide and when you have free parking what more could you ask for, when everything is within a 10-minute radius?