There are 48 urban centres in Australia that have more than 25,000 people - so you are limiting yourself there. And you don't want a big city (whatever that means - let's say it excludes the Gold Coast - which is larger than Hobart - Newcastle, Woollongong...Geelong - anything larger than 100,000), and Tassie and NT, so you are down to 26 places in Australia that fit just two of your criteria - see
https://en.wikipedia.org/wiki/List_of_cities_in_Australia_by_population. If you visited them all for two weeks, it would only take a year, and you would have sampled every possibility!
Coastal Queensland is beautiful, but gets cyclones and floods. It's also tropical rather than Mediterranean.
Toowoomba - a bit on the cold side.
Ballarat - almost a dormitory suburb of Melbourne, gold history, it and Bendigo are very similar, with similar history. Ballarat is colder in winter, and my grandfather said it was the coldest place in Australia.
Bendigo - great place, good hardware stores. A bit pricey, because it is closeish to Melbourne (good train service to Melbourne, and bus to Tullamarine airport) lots to do - you should go to their Easter parade, where EVERY SINGLE community group parades, along with the Chinese dragons (longest Imperial dragon in the world, and oldest Imperial dragon in the world) and all the lion dancing teams from all around Australia - it goes for HOURS.
Albury-Wodonga - another good place with lots to do.
Mackay - gets very wet. Tropical. Definitely not a Mediterranean climate.
Mandurah - isn't it really part of Perth?
Maitland - probably part of Newcastle.
Bunbury - didn't seem to have much to do there, but I wasn't there for long.
Rockhampton - another tropical coastal city. Interesting place with a variety of things to do, but I don't like the small biting wildlife.
Bundaberg - ditto.
Hervey Bay - too tropical, too touristy. Was once nice. Beautiful place.
Wagga Wagga - a bit too flat. Has a lot of things going on. It gets a little too hot for me.
Melton - part of Melbourne.
Coffs Harbour - mentioned above. Was once nice, but too touristy. Wonderful scenery.
Shepparton-Mooroopna - too flat. Gets floods. Great people.
Port Macquarie - haven't been there that I can recall (I must have). Lots of people like it.
Tamworth - it's an inland town. Has a festival. Is in northern NSW where it is pretty.
Orange - ditto.
Mildura-Buronga - Nice place, lots to do, but it gets pretty hot.
Sunbury - really part of Melbourne.
Pakenham - really part of Melbourne.
Dubbo - another place in NSW that's flat. People often say it is in Western NSW, because they don't count most of the state. It's a nice place, with lots to do, and it's a gateway to the outback (like Mildura is, but I think Mildura is nicer).
Gladstone - another tropical coastal Queensland town with biting insects.
Bathurst - Nice place, lots to do there, as it is sort of at the back of the Blue Mountains. Rather isolated though.
Kalgoolie-Boulder - I haven't been there but it is probably too hot.
Warnambool - REALLY NICE PLACE. Coastal Victoria (the only one on the list). Interesting place.
Nowra-Bomaderry - A tourist mecca in summer. (probably the same can be said for Port Macquarie)
Lismore - I've been there, several times, but I can't remember much about it.
Albany - Nup, haven't been there.
And I thought I hadn't seen much of Australia!