There are coin operated lockers. (From 300 to 600 yen per calendar day - depending on size) in the land-side area. (Floor 2 or 3 IIRC).

4 hours is barely worth going landside for.Consider that it may take 30 mins+ to clear immigration and customs. And you will need to get back there to clear immigration and security at least 1hr before ETD. That consumes at least 90 minutes of your precious time. Factor in another 15 min to get change and sort out a coin locker... I reckon you have 2 hrs and 15 min to play with (assuming you arrive on time and move fast).

OPTIONS:
Shopping mall amd outlet center just across the bridge. No local flavour - Frequent bus link.

Inunaki onsen ( Hot spring) - I'd take a cab rather than faffing around with public transport for this.