Apple - Disable cellphone network but keep wifi?

You can enable "Airplane Mode" and then turn on Wi-Fi.

For phones that use a GSM sim card (even if they are on CDMA networks), if you remove the SIM card, you disable the cellular radio. Calls and cellular data stop flowing in this case.

This will not disable phone calls, only internet:

Settings > General > Cellular > Cellular Data -> OFF

If you have a GSM version of the phone then you could just remove the SIM card. If you a CDMA version then you don't have a SIM card so you could turn on airplane mode and then turn WiFi on.