Okay, you're visiting NYC and looking for something unusual, yet affordable, to do in the city. It's not for everyone, but if you're into food--real food, not processed, mass produced food stuff--and you've got an adventurous palate, then come to Queens. It's so close to Manhattan--all my suggestions are close to subway stations and some are only a few stops from midtown. Manhattan housing prices are such that Queens is the new immigrant mecca and where all the authentic ethnic food is at! The tastes and communities run the range from European to Asian. The thing to remember is that these are communities, not tourist attractions, but then the experience is real, not contrived.
From the 59 Street and Lexington Avenue station one can catch the Q or the N train and in four stops arrive at Broadway where the train runs elevated, not subterranean. As one descends to street level no further explanation is needed. This section of Broadway is virtually a "restaurant row." Of course, mixed into the restaurants are other shops that cater to everyday living, however, our immigrant communities take food seriously--even the supermarkets stock products that are less than common. The neighborhood has been known as a major Greek hub, but that community has diversified so much that the range of culinary tastes served is quite varied. A place still worth visiting for Greek food is called Uncle George's--it is right on Broadway, as are many others. One will notice an interesting phenomenon here, it is the number of cafes. The restaurants don't have much of a dessert menu. That is because coffee and dessert is an outing and specialty unto itself in Astoria.
At Times Square or Grand Central, one can catch the 7 train into Queens. This train line can lead on a number of adventures into Queens--it has been called the "International Express" and also the "Orient Express." The latter probably refers to the fact that the last stop is Main Street in Flushing, Queens, which is home to the largest Chinatown/Asia Town in the city. We'll work our way there, but not yet. Once the 7 train clears the hub of Queensboro Plaza and gets over into Sunnyside or 46th Street, a number of restaurants appear--mainly along Queens Boulevard, but things really get cooking around 74th Street, which leaves you at the beginning of a town called "Jackson Heights." The range of eateries will hit you immediately. There is a "Roti Boti," and also a Vietnamese restaurant in sight of this station. The real restaurant row of this neighborhood is 37th Avenue where everything from Indian to Argentine Steakhouses can be found. The streets are full of locals. You will be eating with folks from all walks of life. The neighborhood is safe, the service is good and the prices are quite reasonable.
I called this Asia Town and it is, though demographically the Chinese are best represented. The place is great for Dim Sum, but the Chinese and the Indians have an impressive diaspora that has been affected by world cuisine, so there are always surprises. As a Latino, I am quite aware of the Chino-Cubano, but also of Chinese living throughout Latin America. There is a restaurant nearby that serves a mean chicken--they're Chinese from Peru and they haved quite an extensive Latino clientele. They speak excellent Spanish. The same has occurred throughout Asia, so never count out or sum up the Chinese.
Another large community in this neighborhood are the Koreans whose style of barbeque has become very popular. It is a tad bit expensive, but grilling at your table is fun.
It seems to me that the ethnic diversity of NYC ought to be to a tourist attraction. If this is a problem for you, then obviously stay away--no one will miss you. On the other hand, if you really want to travel the world, but can't afford to, come to Queens--it's the next best thing! Your Metrocard is a pass to adventure! Furthermore, you'll find that Queens has it's share of culture. The Flushing Remonstrance was in Flushing, Queens. Astoria was named after the Astors and the Maspeth/Newtown Creek area are the earliest settlements in the borough, or the country for that matter. For a Queens culture guide check out the Queens Borough President's website