Buying new iPad and sharing with an existing old Verizon's iPhone 4S

He would need to purchase a Verizon-model iPad, though it doesn't matter where in the US he purchases it. Verizon-model iPads (other than the iPad 2) use either CDMA or LTE, depending on the service provided in the particular area.

Whether he can use any iPad with his existing account will depend on his specific plan. He'll need to talk to Verizon about that.

Regards.