The Verizon iPhone4 will not work anywhere that uses GSM technology---overseas included. It is a CDMA phone. The Verizon iPhone4s has CDMA and GSM technology. Verizon can activate/unlock the sim card in the 4s to be used overseas only, it will not work in the USA.
I am traveling to Italy in Sept and have investigated this up one side and down the other! LOL! I will be taking my Verizon iPhone 4 to use on wifi, but in airplane mode. I have downloaded Viber to use over wifi for VOIP calls and texting.