Belle Hall looks like a very nice community, I've been through there a number of times. Playground/park, swimming pool, good location, most homes and yards well-taken care of, and home available in a number of price ranges from 200k-600k+.
As to private schools in Mount Pleasant, here you go:
Private Schools
Chesterbrook Academy
1212 Two Island Court
Mount Pleasant, SC 29464
Christ Our King-Stella Maris
1183 Russell Drive
Mount Pleasant, SC 29464
First Baptist Church School
681 Mccants Drive
Mount Pleasant, SC 29464
Montessori Of Mt Pleasant
414 Whilden St
Mount Pleasant, SC 29464
Mt Pleasant Presby Church Lrn
302 Hibben St
Mount Pleasant, SC 29464
Palmetto Christian Academy
361 Egypt Rd.
Mount Pleasant, SC 29464
St Andrews Episcopal Day School
440 Whilden St
Mount Pleasant, SC 29464
The O'Quinn School - East Coop
955 Houston Northcutt Blvd
Mount Pleasant, SC 29464
Trident Academy
1455 Wakendaw Rd
Mount Pleasant, SC 29464
Hope it helps.