The Jolimont train station is across the street from the Hilton in part of the Yarra Park/Melbourne Cricket Grounds (MCG), it's in a depression, kinda under the road.
Two tram lines on street level also take you to the CBD, plus a few buses. Lots of transportation if one needs it.
The myki machines at Jolimont wouldn't take paper money nor debit card even if it has the slots for them. There's a 7/11 down a block on the Hilton side to load up money/buy a myki + snacks for your trips around the city. The Myki is good on the tram, trains and buses. Interestingly the Clipper system (SF Bay area's Oyster/Opal/Myki) picked up I had that card saying something like too many cards registering.
The cricket grounds are a bit farther back from the train station, along with the National Sport Museum inside the MCG. The Fitzroy Gardens are next to the Hilton, very beautiful and includes Capt Cook's Cottage.
Rearranging my trip left me with Emirates Stakes Day for the Melbourne Cup festival. The train takes you right to the track. Got good seats in the grandstand, with a view of the finish line. Even with a hoodie and a jacket, it was freezing in the morning (especially when you're wearing a dress). Drizzled a bunch, luckily the overhang kept me dry and eventually it cleared up. It is a humongous, beautiful track - I've been to Churchill Downs which is one of the biggest tracks in the US, but Flemington dwarfs it.
I didn't book my tours until I was in MEL as I wasn't sure if the weather would hold. First up was the Phillip Island tour with The Little Penguin Bus. Met at a CBD hotel and was dropped off at my hotel later that night.
I signed up for the Penguin Plus package which gets you on a smaller platform (2nd pic) closer to the hills where the penguins nest (basically under the camera in the 1st pic of the regular grandstand), so we saw a couple hundred come up the beach and walk along the walkway, we were less than six inches away. We also had a bit of time before the penguins to see the Nobbies and saw two wallabies playing off the road. No cameras allowed during the penguin walk so the only pics are from the visitor center.
Then I did a 1 day Great Ocean Road tour with Go West. I was picked up and later that night dropped off at my hotel. The tour guide was entertaining (playing Australian kids songs and stories about our locations) and stopped off at a lot of spots to take pictures. We saw koalas, wild parrots, an echidna and a temperate rainforest (saw a flesh eating snail - looks like a regular snail with a black shell) along the way and the biggie 12 Apostles and London Arch.
It rained on my last day so I did a tour of MCG, National Sports museum, and the Melbourne museum before my flight.
Skybus picked me up for the airport right when they said they would, transfer at Southern Cross for the airport Skybus was quick. I was very impressed as they were very efficient.