Most public schools in Mount Pleasant would be rated as "good" or better. So, you'll just need to settle in on an apartment complex or a rental site for condos or townhomes that are being rented out by owners or property managers.
Mount Pleasant Apartments for Rent - Mount Pleasant, SC on ApartmentGuide.com would work, as well as hooking up with a property management company that is renting out homes, condos or townhomes. Carolina One has a property management division, and you can find a list of their rentals available through the local MLS here.
South Carolina Homes and Rental Properties. You can also find a list of all rentals available through the MLS here,
Welcome (http://mls.charlestonrealtors.com/Navigator.aspx?CurrentPage=Search%20Properties - broken link) .
Best of luck!