After looking around at several other sites in the city, this seems to be your best option if staying in Naha. Located on the ground floor of the Estinate Hotel, they offer daily, weekly, and monthly working passes for using their ground floor lobby and lounge area.
A weekly pass costs 7,000 Yen (£35), while a single day pass is 2,000 Yen (£10), both giving you access from 8:00 AM to 10:00 PM. Although not a conventional office space, it makes for a surprisingly comfortable base with a few large desks and a central area with stools. There's an outdoor seating area, which is a good option on sunnier days.
Each pass includes three complimentary drinks throughout the day (only one being coffee) and a complimentary hour of free beer from 5:00 PM to 6:00 PM, which may come dangerously early in your work day. There's an on-site cafe specialising in tacos, ideal for evening snacks.
Some downsides are the lack of a dedicated area for sensitive calls and a noisier-than-ideal general ambiance. However, assuming you're a short-term visitor, neither of these should deter you.
Other options In Naha
HAVE A GOOD DAY - This site only recently opened and looks like it could be an ideal work-oriented place. At the time of visiting, there was no one in the entire building, which led to a bit of an empty ambiance. It has great potential though, so I would suggest poking your head in for a walk around as it begins to gain traction. It closes at 20:00 in the evenings.