There are a lot of countries that rely on tourists so that they can get more money. People will visit their tourist spots and this can be good for the economy. Americans hold one of the strongest passports in the world but it seems that there are some countries wherein Americans are being advised not to visit such as the Central African Republic. This country has a violent military coup that will probably not end soon.
Libya does not want anyone from the West to enter their country and America is on the west which means that they should think twice about visiting. Another country that is very strict about foreigners is Eritrea. Securing a visa can be very hard and it may not be worth it in the long run.