People, dont answer what you dont know. I've been playing tennis since I was just that - 3. In fact, I went to university on a tennis scholarship! I loved it during my childhood. I was outside, always had friends around, family supported it, etc. Kids are very flexible and resilient at an early age and introducing them to all kinds of sports is vital to coordination and development.
It will be hard to find a place (normally hotel) where you can find anyone to teach lessons (if needed) - otherwise, work a deal with a hotel which is a quiet environment and teach her/him yourself. Remembering the attention span is very small for your child. But tennis can be made up into a number of games. Good luck.