The Botanical Gardens in St. Kilda are a great place to stay overnight in your car, if you want to spend your time in St. Kilda. From here you are close to a number of hostels as well as showers, which you can find on the St. Kilda beach. Find a nice spot for your car around the park. In the park you also find public toilets.
UPDATE: Readers informed us, that this place is not recommended for overnight stays anymore – there are “no camping” on every corner now! However, if you look for a free parking spot during the day, than the Botanical Gardens are just right for you. There are signs informing travelers that it is not allowed to stay overnight there.