Yvonne,
For me, the weather in Sydney in May is just nice. Weather is just nice, around 15C (even in winter never snow in Sydney), day time still have plenty of sun, just add on 1 layer of fleece top would be enough, I think. Night time could be a bit colder, but it's management. I think to go Sydney in near winter time is good, as their summer is way too hooooootttt!!! Imagine the very old-style train with no air-con at >40C, gosh! Rain? No need to worry much. It won't rain like cats and dogs like here. Even if it rains, only drizziing and that's it.
Public transport generally IS expensive. Get the special ticket for travelling, like 3 days unlimited rides for train/bus/ferry, very good value for money. For a good harbour view, don't join the ferry tour, it's pretty much a waste of money. If you get the unlimited travel pass, just get on one of the ferries and you will have pretty nice view (similar to those if you pay for a special tour). Or if plan to go the Zoo, you have to take the ferry and the journey will give you a good view of the harbour bridge. Taxi is also VERY expensive.
Food wise, many different varieties and pretty easy to find food, Thai and Japanese (takeaway sushi particularly) food being the most popular, prepare to pay about AUD$10 per person. for a simple lunch, sit-in dinner, expect to pay AUD$30 per person. There are restaurants around harbour bridge on a high building give you fantastic view, but those will burn a hole in your pocket.
Too much to talk about........maybe you tell me what you want to know in particular?