HND is close enough to the city that you actually have time, with 4 hours, to enter Tokyo if you like.
The Keikyu Line train will take you on a 10–15 minute, 410-yen journey to Shinagawa, which is itself kind of gritty commercial and boring but has some nice little parks and, at certain times of day, an amazing view of salarymen commuting. (Walking in the opposite direction from everyone else at Shinagawa to/from the Shinkansen tracks feels like being a salmon swimming upstream.) There's a solid set of food stalls near the station (although plenty of food at HND airport too, so don't go out of your way.)
There's a good rail connection from Shinagawa to Shinjuku or Shibuya (15-20 minute journey), both of which are great for wandering around aimlessly for a little while if you like that kind of thing. (I thought the yakitori stalls in the alleyway next to Shinjuku station were really cool to see.) You can also get to those more interesting places via monorail+train — consult your map or a local for directions.
You probably also have time — although it would be a bit tight — to walk to the Tokyo Metropolitan Government Building observation deck near Shinjuku station, open daily with last admission at 22:30, and accessible in as little as 46 min from HND depending on the route you take (consult Google Maps, which is fine for this). Great views from the 45th floor, free!
It all depends what kind of thing you like. HND airport is also perfectly fine airside (or landside) retail and food.
But I once had a great time on a 4h10min layover at KIX which we spent actually entering the suburbs and seeing some of the country, and with 4 hours at HND I think you similarly have time to explore a little bit if you like. Why go somewhere if you're not going to go there?
(This is kind of a hypocritical opinion because I just spent 5 hrs airside at CGK…)