grammar – Why do we say “I’m at home”, but “I’m at the gym” instead of “I’m at gym”? – English Language & Usage Stack Exchange

This is a case of idiomatic expression, particularly in American English. But, it relies upon the specificity of the location in question.

British English has more examples of places that don’t require a definite article. See this question

As a rule, home without an article usually defines a specific location. That is, my home. If you were at a friend’s house you’d say the home of a friend. (Ironically, you’d still say I’m at the house even when it’s yours ….)

The same applies to school. I’m at school means I’m at the school I always attend. I’m at the school implies that it’s not a habitual location for you.

The same applies to Nome, Alaska. I’m in Nome, Alaska. Not the Nome, Alaska. So, it seems to hinge (in AmE) on the specificity of the location.