simseema17,
i am unsure whether or not you are still an undergrad, but if you go to the career development center at your college, they should have a wealth of information on summer research opportunities. off-hand, i know that there are summer research programs designed for undergrads (usually the summer preceding senior year) at rockefeller university and albert einstein college of medicine (yeshiva university); i have completed a summer at the latter institution. i would suggest contacting the universities directly and ask for such positions... most of these opportunities are paid. however, if you are a senior already... perhaps you can apply for a research associate position during the year in interim; i believe you are applying for 2003.
good luck, simseema. if you are willing to move out of the city, i would also try the national institutes of health. they definitely have a summer program.