I have a myq garage door opener. My garage is way out in the woods. I do not have internet access but I have setup a wifi router. Is there any way I can operate my door without a internet but wifi connection?
Without an internet connection, it would basically be worthless.
If you used the Wink home automation system, you MIGHT be able to use the opener controller from GoControl. Wink can support controlling some things like lights if the internet is down... just not sure if it would work with the GoControl. Wink does have support for the Chamberlain opener... but it's such a mess right now, I'd not bother with it.
Best to use some outdoor rated access points for your wifi and run a few meshing your home internet all the way out the garage it would probably cost maybe 200-400 usd to do that depending on the distance to that garage.
Having internet will allow you to remote control from away you home internet and get status updates and firmware updates.