Looking for an apartment in Jamaica is not quite as stressful as it can be in many other parts of New York City. However, as in most of the city there is no time of year to search that is much easier than any other. There may be a slight advantage to looking around October or November, but the real key is just giving yourself enough time to do a thorough search for the best place.
If you've never rented an apartment in New York City before, it is worth considering using a professional agency to help you with your search. An agent is useful because they know the neighborhoods, and for the uninitiated in New York, understanding which neighborhoods, or pieces of neighborhoods, might suit your needs can be very confusing.
Jamaica is attached to the unparalleled New York City public transportation system. From the Jamaica Line, you can gain access to the rest of the NYC subway system. There is also an extensive bus network in Queens. With traffic conditions as they are in NYC, and this excellent transit system typically only steps away, most Jamaica residents opt to ride instead of drive.
A historically black neighborhood, there are some cultural facilities in Jamaica celebrating the heritage of its past and present residents. The Afrikan Poetry Theatre is both a performance and a learning venue. The Jamaica Center for Arts and Learning is a cultural hub for this part of New York. If you're looking to do some shopping or grab a bite to eat with some local flavor, just start walking down Jamaica Avenue.