Walking distance? No, unfortunately not. You are right near the water in downtown Charleston, but that's not a beach area at all. The beaches in Charleston aren't far away, really, but they're definitely not within walking distance from that hotel. Isle of Palms and Sullivan's Island are both relatively nearby, and worth driving to, though. There are about five major beach areas in the Charleston area.
The CARTA bus system will get you to the Isle of Palms, but you'll have to transfer. Take the #40 bus to Mount Pleasant and then transfer to, I believe, the #402 bus. You may need to call to make reservations. And double check those bus numbers. It's been a while since I've used it. You can also take a cab, but it'll run you about $30 each way.
If you're in historic Charleston, enjoy what that area offers. It's a beautiful area, with amazing shopping, historic homes, creative and highly rated restaurants, etc. It's a great city.
