Haven't been there for a couple of years, but probably not much has changed...
He/she has probably already discovered that any number of the bars for the troops that are located on the Honch (streets Honcho I and Honcho II) immediately outside the base gates have bar boxes in varying degrees of playability. I don't know how many times I greeted the sunrise after playing all night for a few bucks and/or drinks.
However, if it's a true pool hall they want, Yokosuka may not be the place. After quickly tiring of the bar scene but being around long enough to befriend a couple of the owners, I inquired about quality locations, including one I had seen on the main drag. The people in the know made it fairly clear to me that gaijin were NOT welcome. Not necessarily a relection on all Japanese pool halls at all...I have played at very nice rooms in Tokyo, Yokohama and Okinawa and have been warrmly welcomed at all. But none of them were across the street from 8,000 sailors.
Have them check with George - the owner of George's Country Bar on the Honch. He speaks great English, takes care of his good customers and is very friendly. George will tell him if there is a good place where he will be welcome.
If he just wants to try it on his own, the rooms are not hard to find. Just look for the crossed cue sticks with the pool ball below them, usually a 9-ball or a small triangle of balls. 9-ball will be the prevalent game, unless something has changed drastically.