Inside the city of Rome, there was a place called the Campus. The campus used to be a place where soldiers learned how to march and do other soldierly stuff. It was some flat ground near the Tiber River.
After the Roman army stopped using it for training, it became a place where young men could and did exercise. They would have foot races and places to jump. There were even places to practice archery and box. Of course after exercising they would either go swimming in the Tiber River or head off to the bathhouse for cleaning in the pools there.
Roman men liked to show off. They especially liked to demonstrate their ability at sports and soldierly skills. So there were many places like the campus throughout Rome. They also went hunting and fishing. Romans loved sports. They had several ball games where they could compete with each other. They also had gladiatorial type activities.
Women were discouraged from any exercise at all and were not allowed to show off their athletic skills at the campus.