We used to do our weekly cross practice in a high school field. Our course used about a half lap of their running track.
It worked pretty well, and was my favorite section of the course.
It will work and be fun. I'd be careful as some schools are pretty particular about their tracks.
When we started using ours the school was a public high school. After around 5 years, it ended up becoming a charter school and they kicked us out.
Paul