For Americans:

Seoul is a relatively safe city for American travelers. The locals there don't really dislike Americans, especially after all the support and alliances we've had together over the years. Still, while traveling overseas, it is very important to keep on alert and mind your surroundings. You should always keep your head on a swivel, especially when shopping in crowded markets. This is the prime locations where pick pocketers will go to work and try to rob you. There are other places also where you should watch out. If you are going out late at night to drink or just mingle with the crowds, don't go down dark alleys or streets that seem unfamiliar to you. Obviously most places you go will be unfamiliar, but try to figure out a route during the day so you have an idea of where you are going later on. If you need help you should contact the Seoul Police Department as soon as possible, and if it is something very serious get in touch with the United States Embassy. Something to also keep in mind is the fact North Korea could potentially pose a threat to the South, and you should be aware of what is happening in the news while traveling there. There is obviously no immediate threat of a war, but it is wise to keep it in mind.

For others:

Seoul is one of the safest cities in the world, and foreigners are normally very welcome. Pickpockets are not  a problem but you obviously keep your wits about you in all crowded places.  While the water is safe to drink from the faucet, many don't like the taste.  Most countries recognise the high standards of health and hygiene, and do not require any innoculations. Food often includes salads, and these are usually very hygienically prepared. The author is not aware of any issues of food poisoning from such salads.

At night, there are few empty parts of the city and you are unlikely to feel threatened. There are sometimes political demonstations with many people present. Even these are not threatening, and members of the demonstrators may take you to one side to explain what's going on. And possibly take you into a nearby bar and buy you a soju.