Please encourage people somehow to display their default timezone on their own user page, so we could know when to expect him back again? Practically, for those who displayed their location I could look it up, but I guess, for the newcomers this is usually not available at all (the ratio of autobiographer/all user, and users located on various celestial bodies). What do you think?
Time zone isn't enough though. Would you expect them to log in during working hours or during time at home? Different people have different patterns. For me, the one period of time I'm almost guaranteed to be on SO is during my commute, which would be pretty rare.
If you really want to know when someone's often on, and they've been around for a while, you could analyse the data dump... it might be quite interesting to print a histogram for different users, actually...
A bit cyber-stalker....
I think that if people want to advertise their locale in their profile (Location), then fine...
This would require that the system know what the user's time zone is, which it doesn't right now.
Stack Exchange does not encourage personalized communication, and so displaying that information on their user page, even if we could do it correctly and easily, is not something that would encourage behavior the site supports.
Users can use the API and data dumps to analyze user posting behavior and find this information out for themselves - in fact it would make a nice stack app, and with a user script it could appear on the user's page if that's where you want to see it.
One could also write bots for the chatrooms (or scrape the chat logs) and find users that are interested in personal communications, and what time they are available, typically, in the chatrooms.
But those users that want or allow personal communications provide contact information in their user page, so your best bet is to simply use that and communicate via channels other than stack exchange with those users interested in doing so.