For the explorations you're going to do, go with the Int'l Blvd hotels near the airport -- they ARE central & ammenties surround.
Stay at foot of the Ravenel Bridge in Mt P if you're only going up to Summervile once - it's far! (I live 1.5 miles from the Ravenel Bridge, love the area, but it may not serve your purpose this trip).
Forget Ashley Phosphate -- not nice for an easy going weekend - ugly.
Want a slightly luxury/upscale neighborhood experience?
Inn at I'On. A Bed and Breakfast Inn located in Mt Pleasant South Carolina for unique B&B lodging. Nice (but Mt P local)