Our daycare and then elementary school all had a rule that only tennis shoes are to be worn at school every day.
That being said, our daughter was always covered in bandaides. Her first day of kindergarten, we actually gave her teacher a box of bandaides and told her we "did not want her to go through her own stash, so to feel free to use these".. daughter would need them. We are a family of Klutz's. We can walk down a smooth sidewalk and trip. I bump into walls all of the time.. and yes, we all wear glasses..
I do suggest you have her eyes checked. And on the next physical mention it to your Pediatrician.
It could be your daughter is going a mile a minute and does not have time to look. You can ask her to slow down, look at where she is going.. It still could be she is just not very coordinated.. Dance classes will help, but maybe gymnastics would be better..
When you are playing have her walk backwards, one foot right in front of the other walk sideways. Hop on one foot then the other, Hopscotch. Teach her to skip. Have her take giant steps forward, giant steps backwards.. Then have her try these things with her eyes closed. See who can stand on one leg the longest.. then the other leg.. Do Simon says, then let her be Simon.. It can be like your own therapy sessions..