How about American students' European tourist visas?

You can travel freely. No other policy can be applied to the embassy or consulate of the country you are going to.

At present, you can apply for a Schengen visa to the following countries: Austria, Belgium, Denmark, Finland, France, Germany, Iceland, Italy, Greece, Luxembourg, Netherlands, Norway, Portugal, Spain, Sweden, Hungary, Czech Republic, Slovakia, Slovenia, Poland, Estonia, Latvia, Lithuania and Malta. In addition, the following countries can enter the country at will with a Schengen visa because they have no actual border inspection with their Schengen neighbors: Andorra, Vatican, San Marino and Monaco.

Britain and Ireland have not yet joined the Schengen Agreement. If you want to go, apply for a British visa.