You can stay in Hackberry it is about 6 miles from the main refuge office, however, there is only one place to stay in Hackberry here is the shorcut http://www.babescajun.com
Sulphur is about 20 miles away but there are lots of places to stay, Hampton inn and Wingate are on the highway going to Hackberry. Both of these hotels are very nice.
I do hope by that time more birds will be down there. Let me say that I do not hunt the refuge so I don't know a whole lot about how to hunt it. (We have property next to the refuge). Maybe someone else will be able to provide more insight into hunting the refuge. I have included the shortcut to the refuge website.