There is a shuttle bus.

It was possible to do it on the net, but I think it can not be done now because it is full.

$40 us. Round trip from Airport to Hilton. Airport Limosine (bus).

To use, yes, not to take.

Dear Valued Guest, Thank you for your interest. This is to let you know that Hilton Tokyo's shuttle bus departs hourly from the West Exit of Shinjuku station (in front of Keio Department Store, bus stop No. 21). We are looking forward to welcoming you. Kind Regards, Hilton Tokyo

Dear Guest, Thank you for your interest. For detailed infromation regarding each of our rooms, please visit our official website via the link above. Alternatively, you can also contact us by phone. Looking forward to welcoming you. Best Regards, Hilton Tokyo

Isetan Shinjuku store? Walk for about twenty minutes.

Hilton Tokyo has restaurants and bars on the lower floors. We do not know the view from the Executive Floor Lounge. I'm sorry. I don't think there is a free access observatory in the building.

I took the subway which was about 3000 yen to Shibuya Station and then took a short Uber to the hotel.