Well walking is great in Sydney, Coogee -> Bondi; Bondi -> Watsons Bay -> (ferry) -> Sydney. The Sydney Harbour Circle walk, also known as the 7 Bridges walk is amazing, and has many offshoots. Go to the link below to download a PDF of it, historical documentation etc. Not sure if you could do that whole walk in a day, unless you start at 7am and aim to finish at 7pm. But you can easily do a portion then get back by public transport (ferry, bus).
http://www.planning.nsw.gov.au/harbour/walking.asp
Those are well known scenic walks - Sydney is generally a great place for Shanks' Pony.
Re pubs, cafes etc, there's loads. Don't know where to start. Asian food, particularly Thai, is almost always of great quality here.
