If you are referring to a park that is a place (e.g. a city park) , then it is definitely 'go to the park'. You could possibly use 'go to park' if you were using park as a verb, such as parking the car. 'you wait here, and I will go to park the car'. Although normally, we would just leave out 'to' e.g. 'I will go park the car'.

"go to the park" is more natural than "go to park". But notice that 'park' here means 'garden'.

Go to the park. Go---to---Park is an awkward and uncommon expression. The definite article, "the" is dropped when the thing that we "go to" is an action. For example: I will go running. I will go fishing. I will go boating. I will to hunting. When I "go to" a PLACE however, the definite article "the" is used, as in; "I will go to the park."

Correction/ 3rd Line, last sentence: "I will go hunting."