Strictly speaking the cheapest option is catching the orange SmartBus from the terminal to Broadmeadows station and then a train to the city. But it'll take forever and Broadmeadows isn't a great area so it's suitable only for cheapskates. Taxi to the city costs very close to $50 each way. Skybus is a ripoff at $28 return for a bus where you're a captive audience for a stream of advertisements, but still may be the best option.

There's hundreds of good places to eat/drink, you'll have to narrow it down more if you want a recommendation. The SkyBus will drop you at Spencer St station which is the dull end of the CBD but you'll be in the free tram zone so you can head up Bourke or Collins St to the more exciting end. Alternatively stroll down to the river and visit the casino if that's your thing (some good restaurants there if you're feeling extravagant... or alternatively some darn tasty burgers at Merrywell). If you want to stroll along a street looking for restaurants I recommend Flinders Lane, starting from Swanston and heading towards Spring. Or just stroll along Southbank.

>Is it better to stay in the city in MEL than out by the airport if you want to go for a wander rather than stay in the hotel?

Well yeah, there's not much to see around the airport, so if you don't mind the trip downtown you'll definitely have a much more enjoyable "wander" down there. If you've got the time and money, go for it.