Inside the city of Rome, there was a place called the Campus. The Campus was really just some flat ground near the Tiber River, but it was a famous area. The Campus in ancient Rome was a place where soldiers learned how to march and do other soldierly stuff.
After the Roman army stopped using it for training, it became a place where young men could exercise. There were foot races and places to jump, and places to practice archery and box. After exercising, the Roman men would either go swimming in the Tiber River or head off to the bathhouse for cleaning in the pools. Many places, like the Campus, sprang up throughout Rome, and in the Provinces, although the original Campus itself was the most famous.
Roman men liked to show off. They especially liked to demonstrate their ability at sports and soldierly skills. Men also went hunting and fishing. 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 welcome to show off their athletic skills, if they had any, at the campus or any other place.