I'm a transplant from Chicago to Melbourne. The weather here is /much/ milder - by Chicago standards, the winters will barely register. This doesn't mean, however, that it's warm enough to swim all year or anything, and the weather here does tend to be somewhat volatile. You don't get a lot of proper, torrential thunderstorms, for example, where rain buckets down for hours. But it's not unusual to have a five-minute random rainblast in an otherwise non-rainy day... The sun is much more intense - there's a palpable, physical quality to it that I didn't experience anywhere in the US, including in desert areas. When it's hot, it can often be humid, which makes the heat more uncomfortable than in equivalently hot locations in the US - and when you have a hot northerly wind... It can be like walking out into an oven. This doesn't happen many days of the year, though - just mentioning it because it's striking when it happens.
Cars aren't needed if you live centrally, or if you choose your suburb with an eye to public transport routes. If you do need one, it's more expensive than in the US - to get the car itself, to run it, etc. There are car share services all over the inner suburbs if you need something occasionally. These become sparse on the ground in mid-range suburbs. Public transport has its ups and downs, but it's leagues above anything that was available in Chicago when I lived there. There are decent bike trails along some commuting routes that will keep you off-road for good portions of common commutes, and biking on the road isn't uncommon, although the relationship of bikes and cars isn't anywhere near as settled or as positive as in some European cities.
Everyday items are more expensive than in the US - particularly if you have optimised your shopping in Chicago's ethnic neighbourhoods... The same strategy works here, though: ethnic markets can be great (although you have to check to make sure it's not an upscale overpriced "atmospheric" shopping location, but a proper market). Aldi is good if you're near one, but not generally as good as the best markets for either price or quality. There's a Costco in central Melbourne now - I haven't checked it out personally, but it doesn't seem to offer anything better than the markets local to where I live (but I chose where I live for the markets and public transport connections).
I've lost track of Chicago rents (I've been here almost 15 years now), but my guess is that housing will be dearer. Utilities almost certainly will, particularly if you have limited ability to make a space more energy efficient if you're renting.
Although this is a sports-mad city in many ways, it doesn't offer particularly inexpensive ways of /participating/ in sports (as opposed to watching them). I was used to being able to score free tennis courts in the US, for example - sure, they were nothing fancy, they might have those metal nets that would go "Ching!" when you clipped them, but they were widely available without charge. I don't know if this has changed in the US, but it's never been the case here. Public swimming facilities are also more expensive - and gyms, as you've noticed. For gyms, maybe see if some of the university-affiliated athletic facilities might be open to members of the general public (or whether they actually make you prove your affiliation...): they are among the most reasonably priced. Cycling, running and hiking trails are everywhere, though - there's an enormous amount of public green space compared to Chicago - I remember being startled even looking out the window of the plane when I was first flying in...
I've really liked it here, although we will probably retire elsewhere (the exact location depends a bit on how things go with my partner's parents' health). But we have a very well-optimised life here at the moment, and it's enough to give me pause when I think about having to start over somewhere else (and I've lived all over the US and in a few other countries as well, so I have the relocation drill pretty well down...). Then again, quite so /much/ optimisation might not be required in a less expensive place...
