There are a few options. Mt Coot-tha is the preferred options for friends who are lazy and don't want to walk anywhere or who really love hiking and are keen to hike up Mt Coot-tha.
Highgate Hill Park provides great views of the city and I think better views than Mt Coot-Tha.
However for great atmosphere and great views my preference is to take people for a walk along the top of Kangaroo Point Cliffs. Not only do you see views of the river and city you also can admire the numerous public artworks on display.
Jolly's Lookout is a great one for tourists, as you can stop in there on your way to Mount Nebo and some of Brisbane's best pristine rainforest walks. It's also a good way to get some perspective on how close the city actually is to Moreton Bay.