Yeah, Airbnb might be your best option, and being that Matthews is not a vacation destination(I grew up there), just a busy small town/suburb of Charlotte, I'm not sure you'll find what you are wanting even there. I'd also try posting on the city-data forum, see if anyone there has any ideas/info that might help you. http://www.city-data.com/forum/charlotte/
I checked VRBO and AirBNB and there aren't many options, unfortunately. They are building a new extended stay type hotel close to downtown Matthews, but it wouldn't be within walking distance. Super short drive though. I'm not sure of the name. There is a nice Hampton Inn in Matthews as well. Again, not walking distance, but you can walk to restaurants such as Chic Fi la, Bonefish and Longhorn. It's about a 5 minute drive into downtown Matthews.