Char's advise is very good.
I'd say dress as the other people dress. Dont wear a evening gown to the grocery store. In other words dont over dress.
Its hard not be nevous the first time but 99% of the people will be respectful.
I go out several time a week. Most people know i'm a man.
Even in the supposedly mean south I'm addressed as ma'am or miss.
Ive been out with my wife to casinos and shoppings. We do this when away from home. We dont take the chance of being reconized together in our hometown
Just relax and have fun.