Sorry, we don't have any documentation for our REST APIs yet, but I should be able to help out in the meantime.
We don't explicitly store the user's last IP address, but you can could check a user's activity log to see where they last acted from. You can get those from /api/v1/users/USERID/audits. The user ID there can be either the current user or any user if you're logged in as a System Admin. This'll return a JSON object containing a list of Audit objects containing a user_id, a create_at timestamp, the action api URL that the user hit, and an ip_address.
Just a note, in the upcoming May release, that API will be moving to /api/v3/users/USERID/audits due to some extensive backend restructuring that we've done. You can read more about that here.