Hit the speed bag. That is the one that worked the best for me.
Some people in our school will hit the heavybag as many times as they can in one minute. Then just keep trying to increase how many times you hit it. But for me the speed bag was the best tool. I came up with different drills such as moving around the platform while keeping the rythem, or hitting the bag with a 1-2 combo, then a 1,2,3 combo, and 1,2,3,4 combo. then switch the stance and repeat.
In my opinion hand speed is good, but rythem and timing will be more effective than speed alone. But I have always been good with my hands, my feet on the other hand is a different story.
-Jason