Anywhere in the Lafayette area would be best IMO due to the surronding area's having the largest amount of jam sessions and accordion players. It would be a good central hub to stay in.

My wife and I have a beautiful guest cottage on our property near Grand Coteau, LA. We normally rent it on a nightly basis, but can give you a monthly rate. It's in a quiet country location 20 minutes from downtown Lafayette. We renovated the building in partnership with Lynn and Steve Lane, who live in London and run the Cajun Barn venue there, so if you know them you might want to touch base with them about it. Or feel free to contact me.

...And Henry's being modest by not telling you that he's a darn good fiddler and gives lessons on every instrument from the accordion to the zither.

(Actually, I don't know if he teaches the zither, but he's an excellent teacher for most of the other letters in the alphabet.)

Mathew, I think that you and your wife are in for a wonderful experience.
It sounds like you have some flexibility time-wise. You might want to plan your visit to coincide with some major events. First, of course, is Mardis Gras (and the week leading up to it). Or a little later you could easily fit Festival International, Balfa Camp, and Breaux Bridge Crawfish Fest into a couple of weeks. There's also Festivals Acadienes et Creoles in the fall.
Also, make time to enjoy Louisiana's unique natural environment (or what's left of it). Take a tour of Lake Martin when the birds are nesting. Stay in a houseboat for a few nights on Lake Henderson.
You must take dancing lessons if you don't already know th dances!
You'll love it!

If you have no experience with the instrument yet, I would suggest attending a music camp first (Balfa Camp for instance), learn with some other players, then scope out the local scene while you're there. THEN take a year to get better on the instrument, and THEN do your sabbatical to Louisiana.

If you're spending your whole time struggling at a beginner level with the box, it might not be the best way to go. You might feel overwhelm trying to cram a bunch of learning in while you're there, and frustration from the pressure.

If you're already an accomplished musician and pick things up easily, that's another matter.

thanks for all your replies guys.
Henry, I've sent you an email, thanks.