There are hubs that don’t use any Internet at all, but that’s not what most people are looking for because these days people want to be able to use a phone app when they are away from home and voice assistants like Amazon echo or Google home.
But there are a number of hubs where You might need an Internet connection to set up new devices, For control when you are away from home, and for voice assistants, but where once you have rules set up, everything within home can run without the Internet. (whether you need the Internet to set up rules just varies a lot.)
Some of the more popular include the Hue bridge, apple’s HomeKit, Insteon, the ikea Tradfri gateway, and Amazon Echo Plus (Which has a zigbee hub inside). There are also some systems from smaller companies like Hubitat and Devolo. The specific devices that work with each of those systems vary quite a bit.
Hubitat was started by some former smartthings customers A couple of years ago specifically to provide more local processing, and has the closest match to the devices that work with smartthings, although there’s still some variance.
But again, it comes down to the exact details of what you were looking for.