FlexiTime provides a number of ways to make it easy to manage employees who work in different locations.
The easiest way to separate time on the timesheets is to add extra types of Work (e.g. one for each location). These can be coloured differently so that it's easy to spot who's working where. On the Timesheet Summary tab you can filter by work and see the headcount coverage for specific locations.
You can also set up employees with Time Planner access. When they log in they can be set up to see only employees that they manage, or that are doing the work that they manage.
The different types of work can also allow you to specify different cost centres via pay codes for the staff (for waged staff).
If each shop operates quite independently you can potentially have separate FlexiTime accounts for each location. FlexiTime can provide a parent account from which you access the sub accounts and the IRD returns can be collated across the shops.