The Director may designate state archaeological sites and state archaeological zones on private property or on property owned by any county, city or town, or board or authority organized to perform local or regional functions in the Commonwealth provided that the Director secures the express prior written consent of the owner of the property involved. No state archaeological site or zone located on private property may be established within the boundaries of any county, city or town which has established a local archaeological commission or similar entity designated to preserve, protect and identify local sites and objects of antiquity without the consent of the local governing body. Field investigations may not be conducted on a designated site without a permit issued by the Director pursuant to § 10.1-2302.