Sheraton, W and Four Seasons allow dogs....I doubt there is a Four Seasons or a W, but I bet you can find a Sheraton in Myrtle Beach. Some Sheratons have a small charge, some don't. It just depends on the property. (I"m pretty sure W and Four Seasons always have an additional charge.)
When I lived in SC we used to go to MB often. I haven't been in about 10 years, but the last few times I went, we rented houses or condos. Its sad to hear about the pavillion...