"へ" means "to the destination", and へ includes a sense of direction, while "で" means "in the place". Therefore, in this case, 図書館"へ"本を借りに行きます is better, because it means I'm going to go "to" the library to borrow books. By the way, we can also say 図書館で本を借りる/借りた. It means that "I borrow/borrowed book "in" the library.