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.
If you like the idea of meeting new people or have a large space to fill, you can open your gig up to the Parlour Community.
Facebook events are one of the best ways to send out invites while controlling the privacy of your event. Also, don't put your address on you Parlour Gig Facebook event, your guests will be sent your address when they buy a ticket.