One option would be to have an "Arduino in a box with an RFID reader, real time clock module, SD card shield, and LCD display" at each location. Staff each carry an RFID key fob and check in and out as they travel. LCD displays appropriate info as they check in and out. Call that $75 or $100 a location to build.
The trick is easily compliling the information. You don't want to have to open each box at each location and swap out an SD card etc etc everytime you want to read the data. Somebody else will have a good idea about data transfer.
Other option is to switch it. Houses have passive RFID tags read by boxes staff members carry. Like many security guard check in systems. Data can be read centrally assumming staff do some sort of periodic central check in.