Funny idea, but while, for example, the NBA Slam Dunk contest has surprising winners with lots of new and exciting players who bring new ideas into the game and who use their creativity to make it less predictable, something like a Fast Serve Contest would only be interesting between players that usually serve in the same range of speed to avoid obvious predictability. And in such a contest, the amount of creativity would be limited, to say the least. But well, so it is for the MLB Homerun Derby where it's all about bashing (admittedly, also timing) the ball as hard as you can and it's still a success. Okay, it's baseball after all
In theory, I would like the "skill contest" best. It could be done as described by serve placement exercises trying to hit a certain area. Or players could get other tasks like "now hit a forehand lob" or "hit a dropshot as short as possible" to show off particular shots. Things like that, it would be possible! Maybe... But then again, while the NHL or NBA All-Star Skills Challenges can include placement, speed, accuracy, passing and ball/puckhandling exercises in a continous course that can be done in 60 or less seconds, it's harder for tennis to fluently combine multiple exercises and bringing the time factor into the game and I guess it would be more like an isolated shot-by-shot challenge.
Personally, I would love to see such a day with some players showing off some fancy or crazy things/shots that they usually can't do in an official competetive match