I am hoping that somewhere in Active Directory the "last logged on from [computer]" is written/stored, or there is a log I can parse out?

The purpose of wanting to know the last PC logged on from is for offering remote support over the network - our users move around pretty infrequently, but I'd like to know that whatever I'm consulting was updating that morning (when they logged in, presumably) at minimum.

I'm also considering login scripts that write the user and computer names to a known location I can reference, but some of our users don't like to logout for 15 days at a time.

If there is an elegant solution that uses login scripts, definitely mention it - but if it happens to work for merely unlocking the station, that would be even better!