If it were me, I'd just take the Limo Bus straight to HND, check your bags in first and be done with it. Chances are, you'll get to HND by 6pm. You may get there later, or maybe much earlier if your plane arrives early and there's no queue at immigration. Make your plans depending on what time it is after you've checked in your luggage.

If at that point you have >4hrs till your connecting flight, then I might head over to Kawasaki. Make sure you take the right Keikyu train. It's only ~15min ride. Kawasaki has tons of food, tons of shopping. 2hrs there will go real fast. Actually there's so much around that area that, if you're not familiar with the area, you might spend quite a bit of time just trying to orient yourself. The DICE Building right by Keikyu Kawasaki Station is a good spot with Tokyu Hands, bookstore, Uniqlo, drugstore and restaurant arcade. The underground mall connecting Keikyu Kawasaki with Kawasaki Station is even better, and that alone may take up 2 hours. But the restaurants there are hit and miss, and you need to go to the right one. The crown jewel of Kawasaki, though, is the Lazona complex which is a good 10min walk through underground mall and the JR Kawasaki Station provided you don't get lost.

If you have <3hrs, I'd stay put at HND and just enjoy the landside mall & restaurants and the observation deck. The airside facility at HND Int'l is pretty enjoyable actually, and there's no price gouging at shops either. I presume you're flying NH. If you're flying in premium cabin, then be sure to save some time to enjoy the lounge. Even if you had >4hrs, I'd suggest you just hang out at the airport if you're tired. I think you will be, due to the time difference.