I had the same problem after installing FFXIV on a new computer.

It turns out that the game doesn't use the system clock to determine local time, it uses the system TIME ZONE + server time. Your system's Time Zone is probably incorrect.

First, exit FFXIV. You should be able to change it by clicking on the clock, selecting "Change date and time settings...", and "Change time zone..."(in Win7). After that, you'll need to change the system time as well (since changing time zones messes it up). Start FFXIV again and the time should be correct.

Hope that helps!