Well to be honest, an iPhone that cannot connect to the internet can only do the things regular phones do, which are:
1. Texting
2. Calling
3. Camera/video functions
4. Playing music stored inside
5. Notes and reminders (plus calendar)
6. Calculator app
7. Games stored locally
Honestly, it's useless without Internet. If the OP only wants his child to use a phone without Internet, the OP should not consider an iPhone in the first place. Otherwise, it would defeat the purpose of an iPhone. The 'i' is there for a reason.