Hi Brad,
"...(3) establishments providing full service office space, whether on a lease or service contract basis."
You pick a NAICS code based on what soaks up most of your production cost or capital investment, which I think makes this accurate for most coworking spaces. This unfortunately misses the essence of coworking, but NAICS is only updated every five years and misses all sorts of emerging industries at first. Since coworking spaces spend our money on office space but we prefer to emphasize our "product" — community — I'm not sure if NAICS will ever get it completely right.
I think the SIC you'd probably want is 6512, which includes "Office building rental or leasing." The Census' NAICS to SIC crosswalk maps it that way.
I moonlight as a coworker; my day job is for a company that does a lot of niche work with labor market data. This is from the hip and I'm certainly no expert. If you are looking for laser beam accuracy and want to talk with a NAICS wizard, feel free to contact me off list and I'll hook you up.
Chris Aberle