Many European countries border on as many as 10 or more neighboring countries; the United States only borders on 2. No wonder it's hard for average folks to afford a vacation to experience life in another country.
There is one thing anyone can do, though, and that's visit cultural centers within the big city nearest to you. Go spend a weekend or at least a whole day in a place where people speak a different language, eat new foods, and learn about the history and traditions of another culture.
A great way to pick where to explore is to see what other languages your local election ballots come in or the library's web site is offered in. Or call the local library and ask about census numbers for languages spoken. Searching on the web for your city name and "demographics" will probably also give you interesting information (though do consider the source before you assume it's accurate).
For a San Franciscan like me, the obvious choices are exploring the city's Chinese and Hispanic communities. A third of the population is Asian, so there are many neighborhoods full of Chinese restaurants and shops and we have one of the premier museums of Asian art. With a name like "San Francisco", it doesn't take a rocket scientist or a walk through the Mission District to suggest that Mexican and Spanish cultural are a huge part of the background of the city.
Where can you travel without having to leave town?