Public transport is great in Sydney. A train will take you in to Bondi Junction from the city and right on top of the train station there's a main bus station with buses going in all directions. I think it's a 387 bus to old south head road.
http://www.131500.com.au/plan-your-tripGive them any time and destination and they'll tell you the best way via public transport to get there (Some of their ways are a little idiotic so you should flip through the options first. You can even map it.)
Grandma Moses has good pastries, muffins etc. Can't recommend any in specific though when I go I usually buy black bread for myself and a lemon meringue pie for my husband.
Alpha chocolates are chocolates with either mint, orange, coffee, strawberry fillings and according to most taste pretty good. Many people buy them as presents for those back home in the US. You won’t know if you like them until you try them