API for "Last Visited" data of a user

Jim's point is dead on with the suggestion to use the admin console as it will provide the access point of each user and their last visited date. If for some reason you're not able to though - you'll need to leverage the QB API, specifically API_UserRoles and parse out the response. Pipelines can do that pretty easily, there are just some quirks that pop up in the processing if you have users assigned to multiple roles in the same app and how QB returns that JSON data back to you.