You need to research carefully before any visit to Afghanistan. The situation is complex and volatile. Having said this there are certain areas which are considered safe. The Badakhshan Province in the north-east is home to the famous Wakhan Corridor and the Big and Little Pamirs. The safest way to enter here is via the Tajik town of Ishkahsim (border open from 0900-1200, but currently closed on Sundays).
As of June 2013, the road west to Faizabad is considered unsafe by both locals and police (thus you are not advised to use the border crossing from Khorog in Tajiksitan). Heed this advice. However, the town of Ishkashim and eastwards is much safer and has been for some time. The Taliban are despised here so they harbour no friends in this part of the world.
There are two dangers to tourists who travel the Wakhan Corridor. Firstly, the roads are in terrible condition with some dangerous corners that threaten to throw the unwary driver off a precipice. The second danger is the isolation once you reach Little Pamir. There is little or no medical facilities to assist you in case of an accident or illness, and you are days away from such assistance. It is no surprise infant mortality rates are in excess of 40% here. Ensure you bring a well-stocked medical kit when travelling into Afghanistan.
I have heard personal reports about the cities of Herat (near the Iranian border in western Afghanistan) and Mazar e-Sharif in the province Balkh (in the north near the Uzbekistan border) as being both safe with numerous historical sites. Unfortunately, I cannot comment more due to having never travelled there, but plan to do so in the future.
If you wish to visit Afghanistan, it is important to read the following information:
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