You can get a different phone and should be able to get it working with that sim. That being said, if your contract is up, you can modify your plan to remove the data so you are not paying for it.
But here is a warning... if you have unlimited now, one you give that up, you are not getting it back. That also goes for if you get a dumbphone AT&T will probably put you on a plan for it automatically (they can sense your phone) and that will give up your unlimited as well as the only way to keep it is to keep it grandfathered (meaning it doesn't get dropped).
If you don't have unlimited, no worries though as the other plans are current.