You want to build up your core as that is an essential, as you see the pro's and see that they can stop in an instant. The best way to improve your core which in turn affects your balance, posture is to do the 'Plank.' Also if you want to work on rise and fall for in the waltz put your feet together and rise onto toes for the count of 5 hold it for 10 and lower for 5 repeat with just one foot
Any excercise which involves straightening and lowering the knees and feet is the way to go. Also what helps is to stand on one leg with the other pointing to the floor, and with that foot pointing to the floor, write each letter of the alphabet without touching down. To help. Do not think of the leg which is moving. Only concentate on the leg you are standing on. Which is what we should be doing when we dance. We should dance completely from foot to foot. This I have been told.
There are so many exercises you can do that will help you dance better. Build your core strength using any exercises you find that you will do regulary. Friends have taught me a few yoga positions that really help, and I find that doing one-legged squats helps a lot. There is so much you can do, and it will make you feel better over time, as well. There had been some videos on Youtube of Marcus and Karen Hilton demonstrating exercises to build strength for smooth dances in particular, but they seem to have been removed due to copywright issues. They were excellent, but you need the visual of those. Best of luck.
Thanks for all of the advice. Hopefully this makes my practice time a bit more productive. I'm especially going to look for helpful yoga videos.
I went to my dance instructor with the same question, and she told me to make sure I'm always holding frame and posture while practicing my footwork so as not to spend hours teaching myself bad habits.
Initially, I spent extra time memorizing footwork shown on whatever dance instruction videos I could find, but it proved nearly impossible to find good videos teaching standard American Syllabus (taught at my local Arthur Murray studio). I may be be better off just working on what I already know -- I definitely haven't mastered it yet.