As you can see, when you ask that question, you will undoubtedly get many different answers. My Mom and Grandmother in an area that was always considered Downtown Charleston but today many do not consider it to be part of it since their home was on Rutledge Avenue a distance from the "peninsula". What may be more important to your potential home search is looking for the area that best suits your lifestyle, i.e. do you want to be able to walk to Downtown restaurants, stores, etc. As in most questions about real estate, the best answer to your question may be "it depends".
Have a fantastic day and let me know if I can help!
Cheryll Woods-Flowers, Mount Pleasant Home Team
Coldwell Banker United Realtors-Mt Pleasant/Downtown