I am writing a semi-fantasy novel, which is set in medieval India and today's New York. I have never been to New York, and will not be there, for far period. How can I do research to embed the cultural and political references of New York into my novel
Google Maps and Street View is your friend. Take a virtual walk, learn the area, click on local stores, read reviews for these stores, check bus & metro schedules, find out about the parks, etc. If you're interested in more in-depth elements, you'll need to provide more details about the particular elements. But basically, the answer is the same: Researching nowadays is easy with Google. If you're after something really niche (say, how inhabitants of a certain district of New York think about another district), find a NY discussion group or something like that
Google Maps is fine for geography, but your question mentions "cultural and political references." If you cannot travel there, you have to find some way to be exposed to and/or interact with the people there.
Cities have their own personalities. They have neighborhoods, cliques, sections, classes, ethnicities. With New York in particular, you have boroughs, and the personalities and cliques of those geographical distinctions are important. Manhattan is focused on wealth, art, culture, shopping. Brooklyn is more family-oriented. Some neighborhoods used to be grungy and are now full of hipsters. How do people feel about the hipsters? What have they done to the neighborhoods? Is it good or bad? There are neighborhoods which used to be so Italian that they developed their own dialect of the language (a mix of Sicilian and Neapolitan) and now they're full of Chinese and Russians. The Chinese make great neighbors because they're clean and polite; the Russians don't because they aren't. And so on.
There are sports teams and rivalries. Baseball has the American and National Leagues, so you have Mets fans vs. Yankees fans. What borough are the fans in and what are the interactions? The Knicks now play basketball in Brooklyn. How did the locals feel about the stadium being built?
What's the food like? What was invented in that city? What's made a particular way there? New York pizza and Chicago pizza are different things and have different fans. New York bagels are not Philadelphia bagels.
How do people get around? The New York subway system is legendary, but it's also breaking down, and delays are rampant. There's an extensive bus system, plus Uber and Zipcar.
The city is heavily Democratic, but they've elected Republicans before. Relations with the police range from good to murderous, sometimes literally. 9/11 left an enormous, unfathomable, indelible mark on the city which you cannot comprehend if you weren't there. It left scars on the pysches of millions.
This is all not to say that you can't write about New York without being there, but to give you an idea of things you need to research if you want to represent the culture and politics with any accuracy.
Start with newspapers. There's the New York Daily News (a tabloid, but still a real paper), the New York Times (the Gray Lady, the country's paper of record, occasionally stuffy and too far left, solid reporting), the New York Post (trashy Murdoch-owned tabloid, makes stuff up, the U.S. version of the Daily Fail), Newsday covers Long Island and Queens (worlds away from Manhattan). There are magazines as well, but newspapers are dailies, and following a story from day to day gives you the feel of how people are reacting. Try the local TV news as well and watch entire broadcasts from different networks.