So much to see in the CBD. They have beautiful walks along the Yarra, parks, botantical gardens, Shrine of Remberance, Art Gallerys etc. Some nice restaurants down Southbank (river side) too.
St Kilda would be a good place to stay, but I would stay in CBD and that way you can ultise the free tram network.
https://whatson.melbourne.vic.gov.au/things-to-do