Valid values for the TZ variable when using DateTime are anything that matches a valid Olson time zone name, like "America/Chicago". When using Date::Manip they're whatever the Date::Manip docs say are valid. See the "TIMEZONES" section of the docs.
Why did Date::Manip behave as you described? Presumably there's a bug in Date::Manip, or your expectations are wrong and Date::Manip can't do what you want.
How often do you need to parse things like "today" and "two days after tomorrow" anyway? With DateTime, for just getting "today" you'd do DateTime->today(). To format it as above you'd do $dt->strftime('%a %b %e %H:%M:%S %Z %Y'). However, you're strongly discouraged from using short time zone names like "PDT" for anything but display, because they are not unique.
