Depends on where you are from, what you are familiar with, and what you want. To paraphrase the man in the movie "In Bruges", if you were brought up on a farm in Kansas you will be amazed by the tall buildings with elevators (lifts), but if you are coming from NYC, not so much. If you do like architecture, as well as the several skyscrapers that are listed in the guides, check out 333 Collins St interior, and also the ANZ bank nearby that. The bank is inside an old repurposed church building.
Of course there are plenty of shops and also museums and art galleries and a zoo and so on. Depends what you (and your kids) want to see and do. One unusual attraction is Old Melbourne Gaol - highly recommended but can be a little spooky for young kids.
If you want to get up close to a kangaroo or koala, or for that matter a lemur, the zoo is quite good. Also there is a very nice Wildlife Sanctuary at Healesville, but it is about 30 to 40 mile drive from the CBD. It's a nice drive to a scenic region if you have a car, but hard to get there otherwise.
For casual sightseeing with no particular agenda, the city is good for parks and gardens and general strolling around. The city is pretty flat but it is still a good tip to travel by tram. The tourist tram that does a loop around the CBD is free. In the tourist tram you also get a bit of a commentary, and of course you can get on and off as you please. Check out Docklands and the sports stadium there. The tram saves your legs, and you get to see the street scenery, unlike the subway which we also have.
Melbourne is laid out on a rectangular grid at 45 degrees to the points of the compass. The streets are either "big" or "little". For example we have Collins Street and parallel to that is Little Collins St. The trams only go along some of the "big" streets, so from time to time you should get off and check the "little" streets. Little Bourke, Little Collins, and Flinders Lane (or Little Flinders as I think of it). Strangely the Bourke St Pedestrian Mall also has trams running through it - should be called Bourke St Pedestrian and Tram Mall. Go there for your dose of buskers.
If you want to use the regular tram (or the subway) each person will need a Myki card, I believe. Ask at your hotel about the myki Visitor Value Pack which includes "a durable myki smartcard pre-loaded with enough value for one day’s travel in Zone 1 (CBD). It also includes discounts and offers at 15 of Melbourne’s leading attractions, saving visitors more than $130"(from the Myki advertising).
Melbourne is VERY big on sport. The Tennis Centre and the Melbourne Cricket Ground ("MCG", or just "the M") may be of interest. If you are here at the right time the Australian Open (tennis) is very popular and very accessible. Tickets for seats at centre court are booked in advance, but many other types of tickets are available. The M is also used for our own football code called "Australian Rules". Compared to American football you could describe it as semi-naked men running around almost nonstop at full speed trying to avoid getting injured while trying to injure their enemies. There is a ball, and four (not two) goalposts at each "end" of the circular field. If you stay longer than three days, you MUST choose a team to barrack for, otherwise you will have no conversation worth listening to ;-). Can you guess I am not a big fan, though my elder son is a fanatic.
We got churches to see - St Patricks (Catholic) Cathedral, and a historic Synagogue (East Melbourne Hebrew Congregation 488 Albert St) very near St Patricks. Further South, a (CE) Cathedral near Federation Square, which is near Southbank.
As a first-time visitor you should try Eureka Skydeck 88 "Teeter on The Edge, a switchable glass cube that slides you out from the building's 88th floor for unsurpassed views of Melbourne and far beyond."
SkyDeck is located in one of the nicest places to stroll around - Southbank. Check Google maps for photos, although streetview itself is not useful because the riverfront is reserved for pedestrians. Federation Square, Flinders St Railway Station, the Botanic Gardens, and the Arts Centre are all near there, also Crown Casino and entertainment complex. Koko Japanese restaurant in the Crown Centre is expensive but good. They serve a special "cheap" $40 lunch - at about two to four times the price of a snack at a nice BYO or coffee shop.
Near Crown Casino, I recommend a guided tour of the Polly Woodside Tall Ship!
When you want a break from seeing whatever, drop into any BYO (Bring Your Own wine or beer if you choose to) Restaurant, or any little food joint provided it is CROWDED. Especially if the crowd is mainly made up of people of the same ethnicity as the food served there. Melbourne is a very multicultural city (not quite so much as NYC but more than Springfield). In almost any appropriately crowded place the food will be tasty and reasonably priced (but refer to Lygon St, below). If you have a special or cheap beer or wine from a nearby bottle shop you may save some money, but the house drinks are usually not too pricey anyway.
Little Bourke St is famous for tasty Chinese food. Lygon St, north of the city, is famous for Italian. However, beware - although Little Bourke St is popular with both tourists and locals, Lygon St is mainly for tourists who are looking for an experience rather than good value.
Just as a bit of background, Lygon St is the centre of Carlton which has a reputation involving money, drugs, and guns. Check the Underbelly series for a sample: Underbelly
. However, guns are a rarity in Melbourne - possessing a handgun is illegal except for professionals - and the atmosphere is friendly and safe. But be careful around nightclubs after about 1 AM. In Carlton you are much less likely to get shot at than to get injured crossing the street while watching the scenery. My wife and I are planning to retire in an apartment in Carlton - we love it. In other parts of Melbourne you are even less likely to get shot at than you are in Carlton. Seriously, in Melbourne a stabbing is front page news, and not so seriously if someone says a bad word in front of his Grandmother that may get a mention ;-).
Try Urbanspoon for finding a recommended restaurant of your style. It lists about 2000 restaurants in Melbourne city and another thousand or so in nearby suburbs. The variety is great: Kosher, Vegan, African, whatever, within reasonable limits. I got this message: We couldn't find any restaurants for "Innuit".
Speaking of Kosher reminded me - if the weather is fine take a 15 minute tram ride to St Kilda Beach. The beach is on the bay so it is not for surfing, but the whole area is a lot of fun. Port Philip is a very big bay (not as big as Hudson's Bay and not beautiful like Ha Long, but it is a very big bay). Check the shops, waterfront, pier, cafes, get some genuine boiled bagels and terrific cakes. Around sunset you can see fairy penguins, and later in the night prostitutes. Just ask the locals for directions.
Do you like coffee? You are in luck. Almost any coffee shop in Melbourne, especially including Lygon St, is good, especially if crowded. Melbournites go to Starbucks and Howard Johnson only when they get tired of good coffee and want to try something different ;-)
Hope this gives a little insight beyond just reading the guides, and helps you to enjoy your stay.See question on Quora