You can invite whoever you like!
Friends and family is a good place to start. If you get on with your neighbours (or even if you don't...) it's a good idea to extend an invite or at least let them know what's happening.
Facebook events are one of the best ways to send out invites while controlling the privacy of the event. Also, don't put your address on your Parlour Facebook event, your guests will be sent your address when they purchase a ticket.