We know that Number 12, Grimmauld Place was the Order's HQ during the 5th and 6th books. Then it was moved to the Burrow. But what was their first headquarters? My only guess is the home of an Order member. The definitive guide to the Order of the Phoenix and Dumbledore’s Army from Pottermore will give you a picture of the original Order. If you keep going down, you will see an interactive guide to each member. Hopefully, that will help.
Proof from Pottermore or the books is preferred.