I was wondering what are good core strengthening exercises that do not include crunches or sit ups?

Hip exercises: You can do hip flexion and extension exercises which also engage the core without focusing on it.

Kick-boxing: Kick-boxing is an incredible way to build core strength and flattening your abs. It is not an easy thing to do, but once you get used to it, you will agree. Start out with just a punching bag--"hook punches" and round-kicks are great trunk-strengthening exercises. Nevertheless, any exercise is better than none. So, start out small and increase as you progress. Good luck and have a healthy new year.