I visited Sydney and Cairns (as well as Melbourne) on a 2017 vacation.
In addition to running in both cities, I highly recommend you do some water excursions. In Sydney, this should be a ferry ride to, say, the zoo or, better, Manly (or both in one day, which is what we did). We did the zoo in the morning and Manly in the afternoon and timed our return ride from Manly back to Circular Quay to catch the setting sun. This was one of the best boat rides I've ever had the pleasure of taking. And in Cairns, you could do a scuba day-trip or even a multi-day live-aboard (we did the latter) if you're a diver. If you're not I'm sure there are snorkeling day-trip operators. Another thing to do from Cairns is a Daintree Rainforest tour, which included a riverboat ride. Cairns is like backpacker central and there is no shortage of tour agencies offering any type of excursion. (Sorry, you didn't ask about excursions but I couldn't help myself -- it's fun to reminisce.)
As for running, in Sydney you absolutely have to go run along the Harbour, specifically east from downtown toward Mrs. Macquarie's chair and beyond. Run around the Opera House and up its steps, through the Botanical Gardens (lots of paths, though you'll likely exhaust them), wherever your curiosity takes you. If you're up for it, run all the way to, say, Bondi along New South Head Rd, spend the day in and around Bondi, and catch a bus or Uber back to downtown. Or while in Bondi you could walk or run the coastal trail down to Coogee to take advantage of having gotten out there. We walked the trail -- scenic and highly recommended. End your run with a beer at either the Clovelly or Coogee Beach Hotels.
I didn't run in Cairns so can't offer advice. If you're going there soon, it will be quite warm and very humid. Cairns much more downtrodden than Sydney, especially so as soon as you leave its downtown, so I'd exercise caution if you run while there.