Qantas, Jetstar and Virgin fly several flights a day to Townsville.
Once arriving in Townsville, you can get a taxi to the Sealink Ferry Terminal (see timetable: https://www.sealinkqld.com.au/magnetic_island_ferry_timetable.php). This should cost about $15 so if you can share, it is cheap. The shuttle service to the ferry terminal has ceased operation, please use the taxi service.
Once on the island, you can catch a bus from outside the ferry
terminal going in the direction of Horseshoe Bay. Ask the driver the drop
you off at the Hotel Arcadia. The fare should be a couple of dollars.
At the hotel, check in at reception at the back of the hotel.