Home Automation without "internet?"

Ok guys-

I'm a total noob to home automation, but I'm looking at setting up some lights and other things I can control via my phone.

However, I have a question. Due to my location, I get very sketchy internet. Yep, in the days of Google Fiber, I'm forced to use a T-Mobile "hotspot."

So, what I'm wondering is could I setup a wireless network for my property without having reliable internet? I understand I wouldn't be able to control the lights away from home without decent internet, but I'm more looking towards controlling lights while I'm home.

I have a detached garage that is about 100' from the house. I'd like to control the exterior lights on it from my house, or while I'm walking to the shop.

Is this a possible goal or am I just fooling myself?