Depending on the timing, you might be able to take the HND airport limobus to the Andaz for about 1300 yen one way and do their buffet breakfast (note that I'm not sure whether people who aren't hotel guests are allowed) and enjoy the views from one of the tallest buildings in Tokyo. There's also a lobby bar/restaurant next to the buffet breakfast area as well as an even higher bar on the top floor with an evening only small sushi restaurant that I think only has eight seats. If the bus schedules don't work, I think it's about a 7,000 yen taxi fare to/from HND and can take as little as twenty minutes.

Or generally take the limobus with a convenient schedule to a conveniently located major hotel (it would be better to pick an area that's not too far from HND) and then walk around the area, such as the Palace Hotel, Peninsula, Imperial, etc. for the Imperial Palace Gardens and Tokyo station area, also close to Ginza