You can determine the exact direction of the Qibla on two days of the solar year while in the Northern Hemisphere – when the noon prayer times on these two days in Mecca will be so that the sun will be directly above the Holy Ka’aba.

Where ever you are, if you can see the sun, and if you stand facing it (or have a stick indicate the exact direction of the sun using the shadow, where the shadow will be behind the stick), that is the precise direction of the Qibla for your location.

Its more accurate than anything else as you can actually physically see where the Holy Ka’aba is, even from the Holy City of Qom!

The two days are: May 29th and July 16th.

Times are: Noon prayer time in the Holy City of Mecca, respective to the dates.

So if you are in the Holy City of Najaf, the times are 12:18pm on May 29 and 12:27pm on July 16.

See here for time conversions.

See page 30 of this PDF file for information from the office of Syed Sistani on this issue.