I'd be inclined towards Melbourne rather than Perth. I live in Melbourne and enjoy visiting Perth (off there in a couple of weeks in fact), but trying to be objective, I think MEL and surrounds has more going for it for the visitor than Perth does.

MEL has fine dining, cheap dining, good fashion shopping (Chapel St), Vic Market, sporting precincts (if you're into that), waterside activities, and day-trip wise, several wine regions (Yarra Valley, Macedon Ranges, Mornington Peninsula etc.), goldfields towns (Ballarat, Bendigo etc.), penguins at Phillip Island. And other things.

PER has wine regions (Swan Valley close by, Margaret River overnight required), some great beaches, some hills, Fremantle is ok, and if you're prepared to go further afield, I'm told Monkey Mia is great with the dolphins, and Esperance is a very pretty place. But they would be overnighters minimum.

And you could slip over to Tasmania quite easily from MEL if you wanted.