First, check this out...
http://www.newrochelleny.com/09parking%20app.pdf
The most convenient parking is the NR Transit Center, that's right at the train station. But, I don't know if anything is available.
New Roc Garage is also convenient and only a block away. New Roc Garage has meter parking for the day if you can't get a permit right away. I used to park at Lawn Avenue and walk the three blocks to the station.
Be sure to call the Parking Manager first at 914 654 2189 to see if parking is available.
Forget the streets. The meters don't last long enough and New Rochelle loves their parking tickets.