Mt Cootha is a great place for a family day out, there is a cafe and a restaurant at the lookout. Both are quite expensive but very nice, clean and the view from the Restaurant is worth the cost!
There are some information boards and toilets.
Down the trails there are BBQ areas and more toilets.
Bus 471 from Stop 7 in Ann st Brisbane, runs regularly on weekdays , there are only 4 services on Saturdays and Sundays.
Same bus back or you could walk like we do! We have walked back to the ferry terminal at Regatta and another time we walked back to Roma St. Walking back down means you aren't stuck to the bus times and you can take a detour via the Cemetary and have a wander through the historic graves.
Hats,sunscreen and plenty of water if you take the bushwalk option.
It's not likely that you would get lost but best to print a map http://www.epa.qld.gov.au/media/parks_and_forests/parks/bfp_mtcootha.pdf just in case.
The Powerful owl trail is VERY steep and not recommended for small children or unfit people. Some trails get muddy or covered with water in wet season.
There is also the Mt Cootha Botanical Gardens to visit on the way down