Your clients need to take the subway to the Bronx. In Queens, landlords will accept vouchers in Jamaica, Hollis, Saint Albans and Queens Village. In Brooklyn, try Bed-Stuy, Brownsville, Bensonhurst and East New York. In the Bronx, anywhere in the South Bronx (south of Fordham Rd.)
None of the above neighborhoods are good BUT you need to explain that landlords can legally discriminate against vouchers based on finances. If landlords can easily rent to people who can afford high rents, then they don't have to take a loss because the vouchers pay much less than the regular rents. If your clients had extra money to pay every month in addition to the vouchers, then any landlord would be happy to accept them. However, most voucher holders don't have $500. - $1,000. extra every month to pay landlords in addition to the vouchers.