Bronxville from Newark - The easiest, and may be the least expensive, would be to take the bus from Newark to Grand Central terminal for $12 (
http://www.olympiabus.com/ ) then from there to Bronxville on Metro North for $5.50 (
www.mta.info). Figure about 30 to 60 minutes for the Newark to Grand Central (depends totally on time of day and traffic) and another 30 from Grand Central to Bronxville, plus up to a half hour waiting time for the next bus and train at each, again depending on the time of the day.
The metro north fare is for off peak, if it's during peak it will be a couple dollars each way more. Peak from GC to there is in the afternoons, the return is peak in the mornings.
Probably have to take a cab from hotel to school and train station to hotel