I am a stadium known for hosting a unique sport that often involves horses and mallets. My field is unusually long and narrow compared to other sports venues. I have seen many high-profile celebrities grace my stands, and my history is intertwined with an exclusive, members-only club. What am I?

1. My sport is often called 'the sport of kings'.
2. I am located in a very affluent area known for luxury and exclusivity.
3. My venue design is not suitable for typical field sports like soccer or American football.
4. I am a frequent setting for glamorous social events.