The facility, just a short distance from the Pentagon, is operated by Nooks, a three-year-old company whose website touts a range of services tailored for “the new world of classified work.” Others like it are popping up around Washington and defense-industry centers such as California and Colorado to serve the legion of employees at defense contractors and other businesses with classified clearances. The cost to access these spaces ranges from a few hundred bucks for an hour or two to a few thousand dollars a month for full-time use.