About an hour from Melbourne is the bottom end of a mountain range, called the Dandenong Ranges, it is actually travels half the length of the entire east coast. One of the parks is called Sherbrooke Forest. It’s near the famous Puffing Billy train line.
You can drive there or catch a suburban train (Belgrave line). Loads of little shops, cafes and pubs here. Australia generally has good information about their national parks. http://www.parkweb.vic.gov.au/1park_display.cfm?park=49 Walking information, maps, guides, activities and more. Easy walking tracks, huge Mountain Ash trees on either side.
The facilities are excellent, parking, picnic grounds with toilets, bins, shops, signs and free BBQ’s. Small walks or long, you choose. there was even a disabled walk (ie flat enough for wheelchairs)