Thank you all once again for the great advice. StacyB, yes I am starting to realise that flying from Oz to the US is much harder than to Europe. I think the quickest route for us will take around 36 hours, but NYC might be the easiest entry point. When travelling to Europe we use either Qatar, Emirates or Singapore Airlines - but they all fly via their base cities which are the wrong direction for the US. I am thinking we will need to get to Sydney (we live in Perth) and then fly via an American Airline (United, AA, Delta ?).

Annhig, nice to hear from you again, you have helped us many times on the Europe Forum. Like you, we are fans of train travel, but don't usually made trips any longer than 7 or 8 hours. However, if it is a picturesque trip to Montreal we will definitely consider it. Montreal sounds lovely - I hope we can fit it in our itinerary.

My pleasure Steve. Glad to have helped. in the interests of full disclosure I should say that the train journey from NYC to Montreal takes about 12 hours. There is one train a day leaving at about 7am from Penn station so it's basically a whole day on the train. BUT there is no faffing about getting to the airport, hanging about, and then the same the other end. And an unrepeatable opportunity to see quite a lot of N. America from the comfort of your seat without driving not to mention the chance to meet some locals - I fell into conversation with a lovely NY family just while I was waiting to board the train at Montreal. I should say that the Canadian end was not spectacular but pleasant and interesting. And you end up in the centre of the city of course. But I'm sure you can fly there as well from NYC which might well suit you better.

As for your routing into N. America, have you thought of stopping off in Europe? . [yes of course you have!] Trouble is, whichever way you dice it it's a bl--dy long way. I just about lost the will to live when I realised we were over Ulan Bator with another 9 hours to go on our way back from Oz a few years ago. [our one and only trip to Oz so far]. Never again in coach we vowed for long haul and so far I've kept to it, though in fairness it's only applied once!

Have fun with your planning, whatever you decide.

PS - Amtrak link here. I registered before I bought my ticket in the hope of picking up an offer but they were only for certain journeys [not mine] or two for one offers which were no use to me. it's certainly an easy website to use though. https://tickets.amtrak.com/itd/amtrak

Yes, the train from NYC to Montreal takes painfully long - 12hrs to go 600km, or ~average 50kph.
Other options include bus (also long @ 9hrs)
A direct drive will be ~6hrs.

or rental car/bus/train combo.

If you are going from NYC to Montreal you could stop along the way somewhere like Saratoga Springs (May/June are excellent time to visit), Burlington VT, or if you want mountains, Lake Placid NY. May/June are bug & mud season in the mountains/woods - we typically wait until Aug/Sept to go hiking to avoid the mud & bugs.

This is the schedule for the Amtrak Adironadack train others have mentioned. The Port Kent ferry mentioned by annhig only runs for part of the year. This year it started again on June 13th.
Attachment 2655
I have not taken this train but have taken the Ethan Allen route that also runs north from NYC. The part of the ride that goes through the Hudson River Valley in New York is very scenic. The Ethan Allen schedule could be used for the first part of the trip if you want to break it up and the timing is more convenient.
Attachment 2656

The whole Adirondack trip is very long. I have taken the 12-hour trip from DC to Montpelier VT several times and definitely prefer that long a train ride to even a somewhat shorter bus ride due to more room and the ability to walk around. I would not worry about mud or bugs in May/June unless you want to go out in the countryside, especially hiking.

I grew up in the NYC suburbs, lived in NYC for 3 years and go there pretty often. I go to DC several times a year. It has been easy for me to see different sites gradually over time so it is hard for me to think of what I'd consider "must sees" on a short first-time visit. I will try to put some thoughts together and post again.

Thank you all again for the Amtrak info.
Annhig, we are thinking of flying from NYC to Toronto, spending a few days there and also take a day trip to Niagara Falls from there. Then, we could take a train to Montreal from Toronto which is only around 5.5 hours. I haven't checked yet, but I assume we could then get a flight from Montreal to Vancouver for the rest of our trip (?).
I hear you loud and clear regarding flying coach - but be warned it is definitely a trap moving to business. We have had 5 trips to Europe from Oz. On our 4th trip we decided to treat ourselves to business on the homeward leg. Wonderful! Guess, what happened then? On our last trip we flew business both ways (albeit spent a long time researching for a great value trip). Once you have flown long haul at the pointy end, it is very difficult to go back. During May/June this year we visited China and couldn't justify flying anything but coach. The flight was fine and Cathay Pacific were great, but we DID pine for the luxury of business. Ha ha

For your visit to DC, I recommend the information on the tourist website. The guide book looks good but I can't quickly find a link to it.
https://washington.org/

The site lists 100 free things to do in DC. One that we have enjoyed is the Millennium Stage at the Kennedy Center--a different performance every evening
Upcoming Millennium Stage Live Streams

<<Annhig, we are thinking of flying from NYC to Toronto, spending a few days there and also take a day trip to Niagara Falls from there. Then, we could take a train to Montreal from Toronto which is only around 5.5 hours. I haven't checked yet, but I assume we could then get a flight from Montreal to Vancouver for the rest of our trip (?).>>

Yes I took that train but I don't recall it taking that long though it was definitely more than 4 hours. I followed a tip a I was given to book business/first class and that could spoil you for standard class trains too - almost as soon as we left the station they came round with tea and coffee, then there were snacks, non/ alcoholic drinks, a 3 course lunch [very nice] then coffee and then we were there!

if you find you can't fly from Montreal to Vancouver, then you could switch it round and fly from NYC to Montreal then get the train from Montreal to Toronto, and fly to Vancouver from there.

VT - thanks for the DC TI link, I'll have a look at it later. 100 free things to do look like a good idea.

Yes, thank you VT, I will take a look at that link.
Annhig - that's a great idea reversing Montreal with Toronto, that could work very well. Yes, we have had the luxury of 1st class trains in Europe - but only in certain countries. In Italy and Germany the cost difference between 1st and 2nd class is minimal if we booked in advance. When using Eurostar, Thalys or TGV the cost difference was significant but the those trains were fine in 2nd class anyway.

Glad to help, Steve. I don't know about flights from Toronto and Montreal to Vancouver but I suspect that they are more frequent out of Toronto. I was given the tip to book first class for the Toronto - Montreal train by someone here and if you time it right so that you'll be having lunch on the train, the difference in price is more than compensated for by the amount of [and quality] food and drink you receive.