Mount Coot-tha, located about 7 kilometers (4 miles) outside the city, is known for its bus tours to the appropriately labeled Lookout made popular for its excellent views of Brisbane. If you'd like to avoid the usual tourist humdrum and overpriced restaurant food, then you should try to experience Mount Coot-tha for its multi-use trails. Although the mountain barely earns its name as far pure height is concerned, you'll find some challenging climbs up and even more demanding mountain bike rides back down through classic Australian bushland. The best biking is had starting at the Gap Creek Reserve, while you can combine a number of tracks (Lookout Track, Jacksonia Track, Kokoda Track, etc.) to create your own day-long circuit of the area. Just be sure to give the right of way to the bikers who've already humped it up the hill and be sure to bring lots of water for the exertion.
Also, at the base of the mountain lies the Brisbane Botanic gardens, where you'll can stroll in a Japanese garden or among the largest collection of Australian rainforest trees found anywhere.