I hope to go when the weather is cool enough to don my sweaters and scarves but yet not too cold. I heard Nov/Dec is a good time,
If you want to be able to wear sweaters and scarves then Nov/Dec is definately not the time to come to Melbourne. For example, it's currently mid November and we've already had several days in the last few weeks that have been over 30 deg C. Coolest months in Melbourne tend to be June/July/August, although June also tends to have a high rainfall.
Which part of Melbourne should I stay in?
Pretty much all of the hostels in central Melbourne are able to help you with tours including Ocean rd and Phillip Island. Look for a hostel that has a postal code of 3000 or 3001 to ensure you are right in the center of the city (these are the two post codes for central Melbourne). I would suggest hostels on Elizabeth Street, Flinders Lane, Lonsdale St, Swanston Street, Russel St or Exhibition Street. You'll find that these hostels are walking distance to everything within the city and have easy access to public transport. Msg me if you want some specific recommendations.