If your tripod trips up somebody, expect trouble.. I suggest you wear a hi-vis vest to make your presence known in a maelstrom of teeming, seething mass of humanity that is Melbourne city.
Also expect stickybeaks are annoying types that think nothing of asserting their right to use the footpath ahead of 'obstacles' like photographers — but you might also equally attract just the curious who want to know what you are photographing (next minute, they pull out their mini-digi and peer over your shoulder to photograph the same scene...). I don't really think you need to bring it up with Council (Melbourne City Council) unless you are a professional and will be causing some obvious disruption to public movement, in which case there are permits, fees, insurance and pedestrian traffic control to be considered). The place to avoid putting a tripod is early in the morning and evening peak on the corner of Flinders and Swanston Streets, again at Bourke/Swanston Streets — it's simply too chaotic. Have your wits about you, use common sense (don't splay the tripod with its legs way out where it causes obvious interference and obstruction) and keep yourself very visible.