The Temporal Facility was the facility housing the time machine. It was located in a windowless area of a ruined laboratory and was the headquarters of Project Splinter. It was located within probable walking distance of Philadelphia, Pennsylvania. The Temporal Facility had once been the Raritan National Laboratory, a leading scientific center for temporal research.
While there is no "Raritan National Laboratory" in real life, Raritan Bay is a major geographic location separating New York from New Jersey. Given that other references put the installation relatively near locations such as Philadelphia and upstate New York, it appears that the Temporal Facility is somewhere in the general New Jersey area.
At this time, the Raritan National Laboratory was the only research center in the world that focused on the science of quantum splintering. Katarina Jones worked there on highly theoretical research regarding the effects of time on human cells.
Elliot Jones was also working at Raritan and had developed a prototype time machine that could send objects forward in time, but not back. He gave José Ramse, who had invested heavily in the time-travel project, full and unsupervised access to the machine; Ramse planned to use the machine to return to his son in 2043. James Cole and Cassandra Railly broke into Raritan and confronted Ramse, and Railly and Ramse were both shot. Ramse gave the gravely wounded Railly his dose of the time-travel drug so that Cole could use the machine to send her to Jones in 2043 for treatment.