Hi,
Im from Melbourne!
theres a shop called acoustic center that has pretty good ukuleles. High end ones aswell such as Kamaka.
Heres there website. http://www.acousticcentre.com.au/ The address is also on the site.
Theres also another shop called Lewis Music store
Ukes in Melbourne? Yes, definitely! You'll find many general music shops and guitar shops, all over Melbourne, have some kind of uke range - although finding quality instruments actually in stock can be a bit hit and miss.
I imagine you might not want to trudge all the way across the city to get something not quite ideal if it turned out that you could have found precisely what you wanted in the actual area you were visiting. So...
Which part(s) of Melbourne will you be in? Assuming you're interested in buying something over here: do you want to buy a $25 instrument just for travelling, or are you seeking something of the highest quality? Will you have time to shop around a little bit, or maybe even be able to wait for a particular model to arrive in the following week's shipment, or will you have only half an hour of your entire stay in which to make purchase?
With that kind of information, people here might be able to give you several even more suitable suggestions.
ive also been to lewis music store in the city. its relatively small and maybe i just went on a bad day but the customer service was shocking. the guy that served me acted like a total cock. he wasn't very friendly and seemed annoyed that i wanted to strum the ukes before making a choice to buy one! so of course i just walked away.
instead i went to melmusic and got my latest uke there. they have a fairly big selection for a general music store (there wont be many ukes above $500 though). i highly recommend it. everytime ive gone there, the staff are very friendly, patient and dont mind that i jam every uke in the store before making a decision.