My usual early morning HND arrivals routine:
1) Shower
2) Drop off bags at hotel
3) Breakfast

Book a shower room at the Royal Park Haneda in the International terminal. You can e-mail them to reserve.

There's a lounge chair in the room if you'd like a quick nap, plugs to recharge, wifi, and your own temperature controls if you happen to arrive in horrible muggy weather.
https://www.rph-the.co.jp/haneda/en/
I'd also consider an onsen but enjoy having the plugs & wifi and quiet space before I head out for the day.

Last time I went to have breakfast at Ivy Place in Daikanyama, browsed Tsutaya, and enjoyed walking about the neighborhood. There's some other (mostly Western) places open for breakfast https://bestlivingjapan.com/tokyo-breakfast-brunch/