hi

Australia is similar in size to China. Imagine someone visiting China for 15 days and wanting to see Shanghai, Beijing, Xian and Kunming, travelling by train.
It is possible, but you will be very busy.
Does your 15 days include days you fly in and fly out?

If not, then ok, you'll probably need roughly 3 days in each place, but you can remove 36 hours form Canberra (it is small) and add those on to 'Brisbane+Goldcoast'.

(I assume you are flying in to Melbourne and out of Brisbane/Goldcoast?)

You only want to see cities? Ok, look out of the windows on the buses, to see scenery.

Also consider trains, as you can walk around on those...

Ok, look out of the windows on the buses, to see scenery

Unfortunately the scenery from the window of a bus on the Hume Highway (Melbourne - Canberra- Sydney and the Pacific Highway (Sydney - GC ) is not really all that interesting (though there are plenty of interesting spots near those highways) and the journeys can be tiring. Even the Princes Highway which runs along the coast from MEL to SYD is less than spectacular when seen through the window of a long distance non stop bus.

Consider flying Melbourne to Canberra, bus from Canberra to Sydney, flying Sydney to Gold Coast. It will probably cost you less if booked well in advance, will allow you more time at the destinations you have chosen and will be much less tiring.

Bus s definitely the easiest option for the Canberra-Sydney leg.

i have 15 whole days. I was not thinking of just seen cities. mY idea was to use those main hubs and see the outskirsts, one day trips, that sort of thing..
I am doing the backpacking thing and I really thought doing it by bus was the best ,cheapest way to go... if flying from melbourne to canberra is easier....

I've just checked a couple of the airlines and flights Melbourne to Canberra are a little expensive (around $129 on Virgin in Mid August). A possible alternative would be to fly to Sydney (Jetstar flights in mid August start at around $35 ex Avalon) and bus to Canberra and back (inexpensive if booked well in advance with Murrays and it'd give you a fair look at inland NSW. You may also wish to consider a day trip to the snowfields from Canberra. Murrays probably do this as well .and they certainly have services down to the south coast if you'd like to pop down there and return to Sydney via the coast.

From Sydney the Blue Mountains are easily reached by train. From there the Blue Mountains Explorer bus service may be handy.

I live in Perth, about 3000km west of those places you mention. I can't give accurate advice but would think a bus would be out of the question between Melbourne to Canberra and Sydney to the Gold Coast. as you'd lose 2 days just there. Bus or train between Canberra to Sydney is probably 3 to 4 hours or so. If you stay in the city centres, then all the cities are easy to get around. Spend a couple of days around the waterfront/Opera House area of Sydney, take a ferry over to Manly, the train up to the Blue Mountains. Canberra is full of monuments and Govt buildings, but a nice laid out city but has cold winters (August). I don't know what people do (legally) on the Gold Coast. Melbourne has miserable winter weather but people still get out, the last I heard about public transport in Melbourne was something about the ticketing machines not working. All I can offer is there is a bus company which goes from Tullamarine airport to the city, - l time I used it the fare was about $15 one way.

The reason the bus is the best option between Sydney and Canberra is convenience, as well as price. It links both Sydney Central Railway station and Sydey airport with the centre of Canberra, while both the airport and railway station in Canberra are inconvenienty located on the outskirts. Murray's internet fares go as low as $10.

You haven't given any clues as to your interests but unless there is some special reason for you to visit Canberra I would not include it in a 15 day trip.

Based solely on weather at that time of year, I would spend 3 days in Melbourne, 5 in Sydney and the rest traveling NSW north coast up to Gold Coast.

I think bus is feasible - overnight Melbourne-Sydney then in short hops up coast - but it's really only worth taking bus Melb- Syd if it's significantly cheaper than flying (remember to include cost of getting to and from airport when doing your comparison).