Hi Kat,
I'm not sure if you are wanting something special like a sleeper sofa, or something that has recliners built in?
I was looking at what big chain stores are around you and am thinking that some places you might want to start are La-Z-Boy, Ashley HomeStore or if you're out near Baton Rouge there is Pottery Barn. I'm not sure if your local Macy's has a furniture section or not? Sometimes figuring out what you don't want in a sofa will help steer you to find what you do want. I have owned sofas that are too low, too soft, too firm and too hard to clean -- so with all those mistakes behind me I am pretty fussy!
If you're looking for a sofa without bells and whistles, I have read that looking for stores that offer an 'apartment sofa' (not love-seat), can help you find a ones that are not too deep so will take up less floor space. With the curves of an airstream, the back will likely hit the wall at some point, possibly making the new sofa sit a bit farther forward than the one you have now.
There are a lot of online retailers too, but for something that you will sit on every day I would want to test-drive that in a store!
I hope you find something wonderful!