Toohey Forest is a great place for a day out! (and it's a mere 15 mins drive south of Brisbane city). Fancy a bush walk? You have 30 tracks to choose from ranging from 250m to 3.5kms so enjoy an easy stroll or combine tracks for a challenging day hike. While you're there check out the abundant wildlife (wallabies, goannas, echidnas, birds, koalas). The wildlife may even check you out too!
There are 3 lookouts (Mt Gravatt, Pegg's and Federation lookouts) with beautiful views across Brisbane and Moreton Bay. If all that walking is making you peckish then Toohey Forest also has several undercover picnic spots with BBQs.
If you're a mountain biker then you're in luck. There are cycling trails (single track and bikeway), plus the bikeway connects you to Brisbane city and the southern suburbs.
Make sure you take a map. The forest is big and you don't want to get lost!
Download the Brisbane City Council one here: https://www.brisbane.qld.gov.au/sites/default/files/20150220-toohey-forest-track-map.pdf