I want my kids to have a phone but want to limit there internet access, is there a way to do that
This might not be too much help but AT&T, Verizon, Sprint & T-Mobile offer parental control at additional costs, take a look at the link though I'm not sure how accurate the prices might be or how outdated the article is. There's also software you can buy like phonesheriff or stealthgenie. If you are on Android you could try out some of these software you can download on GooglePlay https://play.google.com/store/apps/details?id=nz.co.softwarefactory.greenforest&hl=en
If you're using an iPhone or iPod, its pretty easy to turn on parental controls and that capability is built in.
On Android its not so clear cut. But here's a link.