Italian island suggestions for a one month stay

Sicily is a good option. The island is large and offers a lot to do and see to keep you busy for a month. I would still split my stay in at least a couple of locations (maybe Palermo, Siracusa, at the very least), as the island is too large to be visited from one base only. Hiring a car is not necessary if you don’t want, transportation options may not be as good as in the mainland in terms of trains, but they have an extensive intercity bus network.

Sardinia has better beaches (probably the greatest in the Med) but is less rich in terms of historical and artistic sights. Also it would be more of a challenge without a car.

Just curious...

Do Australians have to abide by the 90 day Schengen rules?

You may need to keep your trip to a bit less than three months if you're traveling on an Australian passport and don't have dual citizenship in one of the Schengen countries--or are you spending part of your time somewhere like the United Kingdom or Ireland? If those exceptions don't apply to you, you're probably limited to no more than 90 days in the entire Schengen area within any 180-day period.

Ischia = Glitzy which you specifically mentioned as undesirable. Laid back = Procida which is far less touristy, but it’s also small compared to Sicily which would be better than Sardinia since you won’t be renting a car.

I would love to spend a month in Sicily, but it's a large island, and there's no single point that works for visiting all the attractive spots. I'd definitely want multiple bases there. For me the top two would be the Palermo area (or nearby) and the Siracusa area. You'd need more if you wanted to really enjoy Trapani/Erice, Agrigento, Catania/Taormina and the interior. If you want badly to avoid big cities, I suppose you could stay in Cefalu rather than Palermo, but it's about a 1.5-hour round trip between the two, if not longer, and there's a great deal to see in Palermo.

In Siracusa, the medieval Ortygia district is the most attractive location. I don't know how practical it would be to stay outside Siracusa; for most side trips you'd probably have to start by traveling into Siracusa.

Sicilian inter-city buses pretty much stay in their depots on Sundays, so that day needs to be a stay-at-home day unless you can get to your destination by train.

Was just in Ischia last October, and absolutely loved it! Getting around is easy, there are regular buses looping around the island in both directions. Getting there is also easy, just a ferry ride from Naples of about an hour. I would not describe Ischia as glitzy, unlike Capri. Many Italians vacation in Ischia so I feel it has a very authentic feel.

Thank you everyone for your great advice, it’s certainly given me a lot to think about.

On the Schengen visa, I’ll be flying in/out of London spending a few days there either side, so my time in the EU will come in at a bit under 90 days.

Keep an eye out for more posts seeking tips on the other two months of travel. I only came across this forum by chance, and great to know there are so many people willing to impart a wealth of knowledge!