An employee can do what they want on their lunch hour as long as they return in time.

Unless you are Prison trustee. Where you take your lunch is your own business as long as you can be back ready to work before the end of your lunch break. Not in route... not in the parking lot... but ready to start by the end of your break.

Yes. By saying "unpaid" I'm assuming you're either (a) salaried or (b) an hourly employee who punches out for lunch. Once you are "off the clock" you can leave. The reason some companies limit lunchtime departures for hourly employees is that, as long as you're on the clock, there is a risk of liability if you get in a wreck or are injured while off site.

There is always exceptions, more info would be helpful