K.B.
I've driven by Temple Terrace Presbyterian Weekday School and it seems nice. Here is the URL: http://www.ttpresbyterian.com/weekdayschool/
If you end up living in New Tampa, you will not have many private schools to choose from. I have noticed one affiliated with a church on Bruce B. Downs. Perhaps someone else knows what that school is called. South Tampa has some good Christian schools--St. Mary's and St. John's.
Although we have some outstanding Catholic schools in the area, I personally would not (and did not) choose that route for my own son, being that we are not Catholic. I went to Catholic school for 8 years and always felt like I didn't fit in. Although I was Christian, I wasn't Catholic.