North East of Melbourne there's the Dandenongs, with the William Ricketts sanctuary reserve....Absolutely brilliant aboriginal sculptures carved out of wood there....Puffing Billy & Olinda also worth-while for a visit...Then there's the Yarra Valley heading up into Warburton too.
To the North West there's Mt. Macedon & hanging Rock; & if you continue on there's Mt. Alexander & then onto Bendigo with it's Gold Rush history.....From there you can head up to Echuca & see the old Paddle Steamers on the Murray.
Lake Eildon, due North of Melbourne is also great, especially for fishing & hiring house-boats....Mt. Buller & Jamieson, a little further on are also great to see.
If you do the Mornington Penninsula, then Cape Shank is A must....Arthur's Seat use to have a chair-lift, but I'm not sure if one is still there or not....You can also catch a ferry from Sorrento over to Queenscliff & then do the Bellarine Penninsula….Ocean Grove & Barwon Heads are quite nice to visit.
Phillip Island is good if you want a day trip, as the Bass highway is a pretty good run these days....Formula 1 & fairy penguins there....You can then carry on to South Gippy, through Wonthaggi & down into Wilson's Promontory....then head to Sale & the Lakes district....Marlo past Orbost is a beautiful little town & beach.