Guided tours of sites in and around Pyongyang are the only way to do things. It is very rare to be allowed to wander.
One caveat is regarding personal visitors to foreign residents of Pyongyang. They are usually free to wander around, although the Koreans prefer to 'help' in these situations.
Above all, be very careful about photography. Monuments and palaces are fine, but Koreans hate having their photographs taken, unless you get permission first. If you come across a street market, it is likely that everyone will run away including the sellers, as their existence is a tacit admission of the failure of their economic system. This is not, however, always the case. The Koreans will, however, get very nervous, so a lot of smiling is a good idea. You should absolutely NOT take obvious photos in these situations. You are likely to be arrested, and possibly deported. An innocent photo of a market to Westerners is a very serious situation to them at a political level. Not only does it show the shortcomings of the regime, but a picture of abundance in a market will, they worry, lead to the withdrawal of international food aid.
There are many places to go shooting, usually with air guns. The Koreans love to see foreigners try their hand at this, as sometimes unbeknown to the foreigner they are shooting at images of Americans.
More cruelly, you can target live chickens instead for a couple of euros; if you kill the chicken you get to keep it.
Foreigners are allowed to use the main public swimming pool on Saturday mornings, as they are the ice skating rink in winter. Be aware, that if you have an accident, the Koreans will not help you, probably through fear of dealing with a foreigner. It has been known for foreigners to break their legs ice skating, and waiting for hours on the ice while other expatriates try to help if they are even around!
