Thank you all for your replies. I am trying to remain calm and collected. I live in a large town in the southern United States where basically all the private schools having rolling admissions (with maybe the exception of one that I couldn't afford) and no wait lists so that is not an issue here. I visited (and eliminated) several schools before we selected the public school so I will go out and visit the remaining ones. Some of the reasons that we liked the school: (1) the director spent almost two hours showing us the school and answering questions. We met all the teachers (K-5) and were able to go into the classrooms and observe the students. The students seems very happy and engaged. (2) the director says that we are welcome to come in and observe at any time just sign in at the office first. (3) the kindergarten work that was hanging on the walls is more advanced than what my son to currently doing--all the classes were doing more challenging/advanced work earlier than would be happening in our local public school 4) some of the children were setting up science projects in a part of the gym as it was science week. Each student from first-fifth grades does a project and answers questions from the judges. My son would LOVE doing this. (5) we talked to the director about our son participating in the gifted program at Vanderbilt and how quickly he learns. Also that we want him challenged and he is not currently. She seemed unfazed and said they have a few students like this and the teachers keep them challenged. The students are allowed to work ahead.
My dislikes: (1) the school is attached to a church and while I do consider myself Christian, I want my son to be tolerant of differences. I recognize this is my own bias against religion. Nothing at the school or the director set off any warning bells. (And I have toured Christian schools were my alarm bells went off). (2) the library, playground and computer labs are smaller than at the public school. The computer lab is sufficient. We utilize our local library so that is not a problem. The playground is really basic/ small though. But the students do go to gym everyday.
I need to follow up on how much homework is given. I emailed the director after I left and she says it is at the discretion of the teacher so I am going to find out if I can email the first grade teachers and ask directly.