You need to check your employer's policies and procedures to see if they address this issue. Most breaks, if available, are short time wise; hence, they may require you to stay in the building/area. Lunch may be longer (30 minutes-1 hour) may allow you to leave the building/area. If not, you may want to approach your supervisor for guidance. Otherwise, you may contact the Department of Labor, Wage Hour Division, to get further clarification. Much of this depends on your status, that is, whether you are an hourly employee or exempt employee.
If need be, you should contact an attorney with experience in labor law issues. Good luck!
My response here is an attempt to give you general information and direction and is not intended to constitute an attorney-client relationship as perceived by state law.
If the break is unpaid then your employer cannot dictate how you spend that time. They can discipline you for returning late/taking more than thirty minutes. If your employer is telling you that you must remain on the employer's property during an unpaid break then that is probably not an unpaid break at all and you should be paid for that time.
Generally, if you are off the clock, and you are paid for the time you are clocked out (i.e. you get paid for breaks, but punch the clock to keep track of when you take your break and compliance to specified break times), the company can generally dictate that the parameters of your break time. You do not tell us if this situation applies to you, but I would check out the employee handbook.