Number one correct, however the there is a grammar mistake. "Where is the woman shoeS department, please?" should become "Where is the women's shoes department, please?" You need to put an apostrophe after the word women to show it is possessive or genitive.

I'd say both are correct, however, "shoe department" is more widely used.

I believe that here in the United States, most people who go to a department store would ask, "Excuse me. Where is the SHOE department?" ( I believe that most Americans do not like to use unnecessary s's. I believe that it sounds strange to most Americans to say "shoeS department.") If you asked that question, the store employee would probably reply,"Do you want the men's or the women's department?" And you would answer, "The women'S SHOE department, please."

Actually, the best answer would be: "Where is the women's shoes department, please?" We use the plural form "women" because the shoes are for many different women, not just one woman. We use the possessive/genitive form "women's" because the shoes are connected to the women. We use "shoes" because there are more than one size/style, etc. in the department.

2nd ans is the correct