I travelled three months in Iran and questions regarding safety is a bit of a joke now for me. Because I would say it is probably the safest country in the world to travel in if you exclude Japan and Singapore. However I do understand the concern. My family was worried when I entered Iran because what they see in the media and many people in the west think Iran is the same as all the other countries in the middle east such as Afghanistan, Iraq and Pakistan. Which a dangerous place with terrorists. But it would be much more dangerous to travel to London than to Tehran. I feel safer with my belongings in Tehran that I did on my visit to Madrid this weekend. Petty crime is looked down upon and theft and physical assaults, especially towards foreigners, is uncommon.
On my journey I also met several women who traveled alone without any problems.
If you are going to Iran just for Dizin then there is even less need for worrying about safety. Dizin is mainly visited by rich Iranians who drive with their 4WD from north Tehran and Dizin is probably the most liberal public area in Iran.
In Tehran the only safety issue you should really worry about is the traffic. Which is daunting at first sight. Crossing the road is a near-death experience walking through fast pacing cars. It should however be noted that drivers are skilled and do a very good job at dodging pedestrians, so once you get used to madness crossing the road is as easy as a stroll in the park.
Where not to go
What I wrote above applies to areas in Iran where you would go as a tourists. There are however areas in Iran that most certainly should be avoided (even for the normal Iranian). Those areas include the borders to Iraq, Afghanistan and Pakistan. Most notably the area Balochistan which lies near the borders of Afghanistan and Pakistan. Most of the world supply of heroin goes through this area and there is a high risk of kidnapping. Unless you are traveling to Pakistan over land you will have no reason to enter this area. If you however are traveling by car there make sure you get a police escort. Two of my friends did this journey in 2008 so it is perfectly possible.
