Cairns

Avoid the brown stripe along the coast if you want to feel safer, either go far enough out that you feel the spicy geckos wouldn't venture that far (Green Island, Fitzroy most of the time, low isles etc)
Or go inland where they aren't supposed to be able to climb to: Barrine, eacham or Tinaroo.

There's also some cool river drifts for an inflato. Freshwater creek from redlynch valley down to Goomboora park is right in town, or there's some up around Mossman too.

that being said, there used to be a reasonable SUP scene here, and as far as I know no-one ever got chomped, so if you don't mind a little risk you can go off any of the beaches. Just maybe give the rivers and their mouths a bit of a berth.