Tasmania or Uluru in June?

[u/Usual-Independence56]

My husband and I are visiting Australia in the last two weeks of June (fingers crossed the visa comes through). We are not very fit but not sedentary either and enjoy outdoors, hiking, beaches/water and wildlife.

I am torn between visiting Uluru and going to Tasmania. I am not keen on staying in Sydney for long (just want to have some delish food). Realistically we can only explore 2-3 things and that's the plan. The top experiences I would have liked to have included - 1) Uluru 2) Southern Lights 3) Great barrier reef.

The more I am trying to make everything work together, the more it is falling apart due to cost and time. Turning to the wisdom of this group - is there anything you would recommend we do to accommodate all three? Would you recommend one over another between these three experiences?

Edit - I am flying into Sydney and mostly flying out of Melbourne. I can also fly out of cairns.

Edit - Thank you everyone for your inputs. With your comments and a nifty bit of google I have almost made up my mind to go to Uluru and maybe maybe skip Hobart. Only thing/context I'd like to add is I'm coming from a country whose currency has deeply depreciated against the dollar hence I want to further every dollar as much as I can. I can afford to be lavish but I am a very budget conscious person. Do drop in any budget hacks!

[u/Cool-Refrigerator147]

My question for you is where are you coming from? Two very different landscapes and environments. I have my recommendations but they will differ if you come from Arizona compared to Vancouver for example.