Since, after a few repeat visits, there still isn’t a part of Tokyo that truly draws you I don’t see any point in recommending it. I see Tokyo as a fractured city with each of the segments embodying a distinct personality and an echo of the whole. I say this as someone extremely susceptible to its many sirens’ songs.

My suggestion is that you stay near one of the two main Kawasaki City stations (the Keikyu one is more convenient for Haneda) so you have plenty to do in the evenings and go spend your full day in Kamakura which is 30 minutes away. If you want a more metropolitan experience, then go to Minatomirai Station (20-25 mins away) and enjoy the Yokohama waterfront instead (with the option of a short local bus journey to Sankeien)