You know what you should do?
Offer FREE hairdressing and beauty procedures for the whole day! That will surely get A LOT of customers! However, some people take advantage and have no interests in coming back ever again, they just want a freebie, so you need to make sure that you do a great job.
You should offer the free hair/beauty procedures on the condition that they must come back a second time. So don't allow any free hair/beauty procedures without taking their credit card details first, and if they don't come back after 6 months charge them!
Sounds harsh but some people really do take advantage!
As for the invitation card open it with 'You are invited to the grand opening of (insert name here) Salon and we value you so much that we're offering free procedures all day long and free drinks...' perhaps then write the address with a small map printed out then stuck on it perhaps. Also make sure if you follow my plan on the bottom you write in small letters *if you are having a free hair/beauty procedure on the first day it is on the condition you come back a 2nd time. We take the credit card details of everyone who has a free procedure and will charge you after 6 months if you do not come back again*
Best of luck :D
My idea probably sounds terrible but people REALLY do respond to free things. You don't want people saying "Oh look, another salon opening, who cares..." then chucks it in the bin without a second look, and a lot of people do that.