Sorry Rapture, I know my advice always leads you farther south than you would like.... but here are the places that I have found.
Pawleys Island Tavern has live local stuff Thursday thru Sunday. Usually pretty good stuff, Sundays is usually Jazz. Food is pretty good also.
The Island Bar & Grill South (as opposed to the one on Glenns Bay Rd), music is hit & miss. Wait until the nicer weather since the music is outdoors. Decent food, too.
Louis's has a band that performs often called "Deas Guys" that are very talented and draw a good fun +35 crowd. The link is to their schedule. The food is quite good here but a little pricey.
Murrells Inlet has a bunch of places that have live music too... the Dead Dog & Creek Ratz come to mind. Flo's has a Jazz band on Sundays.