I crossed this peninsula on my way from Melbourne and you wouldn't say the towns you come across are particularly interesting. They can even become completely gloomy like Frankston. What's more, all are faced towards the bay, pretty dull in my opinion, no tides, with tiny little dirty beaches.
The most interesting thing on the Mornington peninsula can be found on the other side, in my opinion, on the slope into the ocean, where the coast is magnificent and tremendously wild, the sea is often relentless and the rocks form surrealist figures.
I also really liked riding a bike to the end of the peninsula, to Nepean fort, which offers a stunning viewpoint over the opening of the bay. In short, a pleasant place but I wouldn't necessary play it amongst the unmissables for a trip to Australia.
The Mornington Peninsula, in my opinion, is not a must-see for a trip to Australia, but could make for an outing if you live in Melbourne. Head off there once you've seen the Great Ocean Road, the Grampians or Phillip Island.
Along the road that runs around the peninsula, you'll see pretty beach-front villas where Melbournians spend their holidays.
The town of Mornington itself has nothing interesting beyond its pier, sailing boats and and seagulls... You're better off heading for Point Nepean, the star attraction of the Mornington Peninsula. By railway or on foot (depending on your degree of laziness), you can reach a fort that stands on the strip of land enclosing the bay. An interesting tour (tunnels, cannons, fortifications), a great time with friends and superb scenery await you.