If at all possible, avoid the local cabs at EWR. The drivers tend to be quite surly and give the cab driving profession a really bad name. Your phone should work just fine (roaming charges will apply) on a GSM/GPRS network. 212-777-7777 is pretty reliable, but so are the 666's and 333's and even the 444's if I'm not mistaken. Don't pay in advance, as there are times you'll want to switch co's last minute (ie they tell you it'll be more than 5 minutes, say no thanks and try another company).
Enjoy the city, nice place this time of year.