This is targeted at older tourists who visit Melbourne and have some time to explore by public transport. You will need a Myki card, full fare $6, concession $3. Check your eligibility at the PTV website. $10 credit on your Myki will more than see you clear for a day's travel. Perhaps $5 for a concession.
I assume you are staying in a city hotel and if not, adjustments need to be made.
Every tourist visiting Melbourne will want to travel to St Kilda. There are different trams to catch to St Kilda. Route 96 is the most direct and marginally the fastest and has replaced a former train line. It travels along Bourke and Spencer Streets and terminates at the end of Acland Street, the street being very popular with tourists, with many cafes, cake shops and other things that interest tourists. Apart from the last part, the journey is not so interesting, although it does pass by Crown Casino, if that is your thing.
Along Collins and then Spencer Street you could catch 12 tram, and have quite a pleasant journey through South Melbourne and some bayside suburbs. The final part of the trip will take you past the once modest but now much renovated homes in the expensive areas of Middle Park and St Kilda West. It should be a very calm and relaxing trip, although not terribly exciting. Again, you can catch this tram to the Casino.
I quite enjoy going to Port Melbourne by tram. The 109 takes you along Collins Street and Spencer Street and again past the Casino. It runs along an old railway line reservation too, so it is a quite a quick trip. The terminus is Station Pier, where overseas cruise liners moor, along with the daily Tasmanian ferry. I can't say there is a lot of interest there but there is the historic Princes Pier to visit and you won't be short of somewhere to eat. The map is very out of date.
The creme de la creme of Melbourne tram journeys is from the busiest tram street in the world, Swanston Street, on the route 16 tram which also takes you to St Kilda, as does the 3A on weekends and holidays. You travel down the beautiful boulevarde of St Kilda Road, past some lovely parkland, the army barracks and a number of historic properties, including a large synagogue The route 16 takes you right through St Kilda and on to Balaclava. Balaclava is full of hipsters, Jewish, recent immigrants, mentally unwell and every type in between. From there you be in Caulfield, full of nice older houses and modern expensive apartment blocks, mostly Jewish owned, along with cheaper rental flats. With a couple of twists and turns, you will be in Malvern, travelling along Glenferrie Road with its expensive designer shops, past the huge and historic tram depot right in the middle of the shops and onto the expensive and grand housing that line Glenferrie Road. You will pass by four railway stations on the journey. Numerous other tram lines intersect the route, including the route 8 tram to the most exclusive area of Toorak. After travelling down a steep hill and crossing the train line at Kooyong, you will pass by The Kooyong Royal Grass Tennis Courts, once the home of the Australian Open tennis and the very posh Scotch College, and then climb the very steep hill to reach Hawthorn, a rather mixed area of cheaper and expensive. The tram will probably crawl through Hawthorn to ultimately terminate at Cotham Road in Kew. You will have seen so much housing of those who have plenty and very expensive private schools. International students will have been on and off the tram, as will have old people who rely on trams to get around. There will also be passengers who clearly can afford to drive in their own cars, but choose not to.
Well, you have ticked that off and don't want to make the almost 90 minute return journey to your city hotel. You don't have to. At the 16 terminus in Kew is the 109 tram, which will take you back to town much more quickly. It travels to the city via the expensive area of Kew and once across the river, into Richmond, or Little Saigon as it is at times known. You will also see the grandeur of another boulevarde, Victoria Parade and the grand former Treasury building at the edge of the city before you travel along Collins Street. You might also notice St Patrick's Cathedral as you pass by.
With an honourable mention is the route 55 tram which runs from William Street on past the zoo and through Royal Park parkland. If you use this tram to get to the zoo and you are weary after your zoo visit, catch the much quicker train back to the city.