Lastonealive has fairly well summed up the north, so I'll help with south-east.
Bulimba (young professionals) for bars, cafes and parks and a nice river commute into town or West End (cafes and bars but more hipster than Bulimba)
Bigger blocks and good transport links to be had in Coorparoo and Camp Hill (more family oriented).
As Lastonealive mentions, Teneriffe and New Farm are good options too.
All that I've mentioned are safe although West End probably less so (has a grungier feel to it because it's a proper night spot).