Otemachi station is the nearest to Hoshinoya Tokyo according to Google Maps.

For arrivals day:

After clearing customs and immigration at Haneda, I would look into using a same day Takkyubin service to ship your luggage to your hotel. Otherwise head to the hotel to leave your luggage with them as I'm not sure if the Hoshinoya offer early check in or if they are like most hotels and insist on 3pm onwards.
Rather than then heading across Tokyo to Shibuya for afternoon tea followed by a further 30-40 minute journey to the cat bar for drinks, I would venture out to some of the areas close to the hotel - the Imperial Palace, Tokyo Station, Ginza, Yurakucho and Shimbashi. That way when tiredness hits you are relatively close to the hotel and it also lets you get acclimatised to an unfamiliar city. It would also maybe allow you to re-jig your itinerary to provide more time on other days to explore other areas.