A very popular day trip from Cairns is to visit the town of Kuranda by the scenic Skyrail and return via the historic railway. Kuranda is a little town in the midst of the rainforest, where you can go on walks through the lush jungle, boat along the river, visit the butterfly centre to see the the electric blue Ulysses Butterfly, and weirdly taste the best German Wurst in Far North QLD. The Skyrail and railway both offer great views down over the jungle canopy and canyons aswell as over Cairns and the coast itself.
If you walk around Cairns, you will undoubtedly be offered tours, which at the time of writing were $123AUD. What's less well-known perhaps, is that a tour isn't actually necessary even without your own car; the local Sunbus passes by the Skyrail center. From Lake Street in Cairns, we took the #111 to Smithfield shopping centre. From here the Skyrail is about a 10-15min walk down the highway, but very kindly our bus driver stopped just outside the Skyrail centre for us, so we didn't even need to walk (obviously don't expect this!). If you plan to do this, I'd just double check beforehand that the Skyrail is actually open on the day of your planned visit, as very occasionally they close for maintenance.
If you prefer to just visit Kuranda, or perhaps just get the railway back and miss the Skyrail, you can actually continue all the way to Kuranda itself by bus from Smithfield (the bus stop is on the opposite side of the road, near the traffic lights).
The Skyrail costs $50 one way, and the historic railway is also $50 returning to Cairns station. The bus out to the Skyrail cost us $7, making $107 each vs the $123 tour price, meaning we saved about $16 each. OK, not exactly a fortune, but the bus out and little walk isn't exactly a hardship, so better to have $16 than not right? Also the bus provides a good option for those on a tight budget who only want to do one of the two expensive trips, i.e. perhaps a bus out to Kuranda followed by a $50 return via railway.