I stayed at the Prince Hotel Shinagawa in March - room was spacious, very close to restaurants, shops and trains and took me 30 minutes on the train back to Haneda the next day. Wasn't too much hassle going from the hotel to the train station even with big bags.
I did use the rooftop onsen at Villa Fontaine once I got to Haneda but didn't stay there. I posted about my experience getting to the onsen from Prince Shinagawa Hotel here https://www.flyertalk.com/forum/35108700-post12.html