The best area to stay in Birdsville is generally within the town centre itself, as it's a small, compact community.
Birdsville is a remote outback town, and its "centre" is essentially the area around the famous Birdsville Hotel and the Birdsville Bakery on Burt Street. This is where you'll find the main services, including the general store, fuel station, and visitor information centre. The town is very walkable, with most points of interest just a short stroll from each other.
For all travellers, staying in the town centre is the most practical option. It provides immediate access to the iconic Birdsville Hotel, which is a must-visit for its history and a cold drink, and the bakery for a classic curried camel pie.