If this is your first time in Melbourne, then I think you should visit some of Melbourne's heritage buildings such as the Royal Exhibition building, the Old Treasury building, the Royal Botanic Gardens, Shrine of Remembrance, etc. There are free guided tours and public transport for tourist around the city. Visit the Cooks Cottage, Schwerkolt Cottage, or join in the Night Tours to see Old Melbourne Gaol and step back in time as you explore some old shades of life.
For restaurants, you can easily find everything from Asian cuisine to European dishes around the city central. You should try kangaroo meat, which is one of Australia's specialties. However, if you can spare a day to visit Yarra winery and taste some of the local wine, I'm sure you will find the trip worthwhile.