Haneda airport to Hakone to Tokyo

hi,
I will be arrive very early morning to Haneda airport, I plan to go straight to Yumoto station from the airport.
then I will stay in Hakone for a day then go to Tokyo the next day morning.

I was wondering what the best way to travel is, I understand there is a return ticket I could buy from Tokyo on the Shinjuku Romance car, but I think it's easier to go straight to Hakone without travelling through Tokyo, would I still be able to get the one day pass for travelling around Hakone? And I got a ICOCA last time in Japan, I can still use this around the buses of Hakone and Tokyo? Would it generally be cheaper than the one day pass?

sorry for the many questions. many thanks!

Have a look at a map. The airport isn't far off Tokyo. I'd be more inclined to say it is within the Tokyo greater area.

Any service whether monorail or Keikyu will require you to head towards tokyo before heading towards Hakone/Odawarra.

Use hyperdia to decide what will work best for you.

www.hyperdia.com/en

Haneda Airport is within Tokyo proper.

Regardless, if you look at the train routes you must travel through the city. The most direct routes require transfers at Shinagawa and Odawara, but you'll probably save money by going the more roundabout route via Shinjuku instead and using a Hakone Free Pass.

would I still be able to get the one day pass for travelling around Hakone?

There is a Hakone Free Pass version that you can buy from Odawara, but the savings won't be as great.

And I got a ICOCA last time in Japan, I can still use this around the buses of Hakone and Tokyo?

Yes

Would it generally be cheaper than the one day pass?

There are no discounts involved with an IC card, but it can still potentially be cheaper since the day passes are so hard to make pay off.