And if you haven't bought plane tickets yet, LGA is much closer to Bronxville than EWR. There are good (and cheap) airport hotels by LGA, from which you can just take the M60 bus to 125th St and Park Ave in Harlem (Manhattan) and take the Metro North from there.

HPN is closer still. If you or your friend are over 25 and can rent a car at HPN, that might be the easiest (and maybe even cheapest) thing to do.