"The" can refer to a type of thing: "The cheetah is the fastest land mammal".
It has a particular use with places, and you will often hear people speak of "the gym", "the shops" and "the pub", for example, even when the speaker does not have a particular place in mind. They probably do have a particular gym in mind, but they might not be thinking of a particular pub:
A. Shall we go to the pub?
B. That's an excellent idea.
A. Which one, the Red Lion or the Cock and Bull?
B. How about the Swan?
Options B and C don't work, as "shopping" is an activity rather than a place, so it does not take the preposition "to", and "home" is exception among places and it, too, does not take the preposition "to".