Since berries are hidden items in the game, you would really need to go around, check, and click A in like every bush or flower patch you find. It is not guaranteed you will always find one but this is typically where it would be - but places like the Cerulean Cave will have berries underneath the ground in which they would then need to be dug up.
You can take a look here to see all the types of berries as well as their location. If you want to boost your chances of finding berries, have a Pokemon follow you - but don't choose ones that you can fly or mount on because I believe they are specifically for those purposes. Simply, choose a Pokemon that follows you and every now and then when you searching for berries, your Pokemon with get an exclamation mark and direct you to a hidden item where you can potentially find berries. As for berries underground in caves, Pokemon that follow you can help you uncover them as well.
Hope I helped! :)
