The Lone Pine Koala Sanctuary is about a 20 minute drive away or you can catch a river cruise boat from downtown. The major theme parks - Dreamworld, White Water World, Warner Brothers Movie World & Wet'n'Wild are all about 45 minute drive (or train) at Coomera, which is on the highway to the Gold Coast. Seaworld is on the Gold Coast at Main Beach. Australia Zoo is at Beerwah, on the way to the Sunshine Coast.
1-2 hour drive: The nearest surf beaches of the Gold Coast (Surfers Paradise) and Sunshine Coast are just over an hour's drive away, or head a bit further to Byron Bay, another hour south of the Gold Coast. There are also beautiful hiking areas in the Lamington & Springbrook National Parks behind the Gold Coast or the Glass House Mountains near the Sunshine Coast.