As many pairs of bonds as possible. Target and big w are sometimes cheaper than from the bonds shop itself (which is in Melbourne central shopping centre) and have different colours.
Aesop do lovely stuff, some of which is good value, plus they do post-poo drops which make me giggle. If you get them to gift wrap stuff they do it beautifully.
Pawpaw ointment and a lovely mint lip balm which you can get in chemist warehouse, name temporarily escapes me but it's nothing flash.
Daiso is good for all sorts of novelty tat you didn't know you needed, I wouldn't make a special trip but if you pass it definitely go in!
Emporium in Melbourne is good for a wander (big, very fancy, new mall with big name shops), brunswick Street has zetta florence which is a gorgeous stationery shop, plus lots of other places to stick your head in, and about 5 million coffee shops.
Oooh, just remembered, you must go to gewurzhaus, original branch is lygon St but in the cbd too now. Not s&b but beautiful beautiful shop.
More generally in Melbourne, go for breakfast out all the time, go to vic market for sure, if it's your thing try and find some of Melbourne's laneway bars, they are hidden but fantastic. Walk along south Bank to see the crown flames on the hour in the evening.