I am brand new in Sydney. How is Dundas Valley connected via public transport?

Dundas Valley is a very quiet and peaceful area, with many good schools and playgrounds close-by. It is well connected to Parramatta, North Sydney and CBD by buses and trains. Trains from Eastwood Station are frequent and fast (20 mins to Central). Lots of free parking near Eastwood station.

To the City: Take a bus (or drive) to Eastwood Train Station. From there there is a direct train to the City. Eastwood is also convenient to do some shopping...they have very good veggies and fruit shops and also butchers. Eastwood Train Station has two entrances. Parking can be tricky sometimes depending on the time you travel, but you will always find a spot, only that you have to walk a bit more. Try to park on the Library side, around the football fields...lots of streets to park.
To Olympic Park: Take a bus (or drive) to Eastwood Train Station. From there take a train to Strathfield and change lines for the line that goes to the Olympic Park.
From Eastwood you also can take a bus or train to Chatswood and from Chatswood you can go to any station along the North Shore Line and finally to the City.
Do not take the train from Carlingford Station because it takes too long and even to go to the City you have to change lines.

There is not always parking in eastwood unless you are arriving before 7am. Sometimes you need to walk 5 blocks.
As for taking a train to homebush, its certainly a long way to get there. Homebush is only a 5 minute longer journey to drive than Eastwood. If you have a car then why not drive for 5 extra minutes instead of the walk after parking in Eastwood and catching 2 trains which are highly unlikely to be timed at similar times so you will probably have a 15+ minute wait between trains.