What are some good exercises for a runner while a broken foot is healing?

Talk to your Doctor. Depending on the bone injured and whether or not you are allowed weightbearing or are in a cast can change the suggested exercises. Talk to your doctor to see if you can be permitted water therapy, which provides a great cardio workout without the impact risk. Upper body exercises are also a good option as well.
Upper body and rest. If you have a broken foot, the most important thing you need to do is rest so you can heal well. You can still train your upper body which will give you more strength, stretch and also do more visualization of your running ability. This has been shown to be a great way to maintain skill and ability when recovering. As you get closer to weight on, you can use a reclining bike, w/cast cover.