Rushcutters Bay is a beautiful spot with decent parking, close to the city, making it a popular wharf for charters. Many charters start from D'Albora Marina since there are a number of charters boats moored there. Boats without access to this private Marina, may be able to use Yarranabbe wharf just north of the marina.
There may be fees involved in picking up from Rushcutters Bay, enquire for more details.
There is some street parking on New Beach Road as well as the surrounding streets within walking distance (you might have to go over the hill).