Hobart would have to be one of the healthiest and safest cities in Australia. Still common sense prevails, as it does anywhere you travel in the world.  Perhaps the biggest unexpected danger to your health here is sunburn.  Because temperatures are usually cooler than elsewhere in Australia, even though the UV index is high people often don't think to cover up with sunblock or a hat until it's too late!  Make sure you slip-slop-slap and try to avoid the worst of the sun between 12 and 2pm.