I had an injury to my knee ago while playing football, I was thinking of asking users about exercises that would be good to strengthen my knee perhaps based on their own personal experience. Would this type of question be suitable on sports exchange or is there another site that would better handle it?
Asking these kinds of questions on Sports SE would be fine as related to a specific sport. Thus, asking questions about playing football with regards to your rehabilitated knee would suffice.
In addition, general rehabilitation questions would suffice at Fitness SE. Their on-topic help center page states that "injury prevention" is on-topic, and could be related to "exercises that would be good to strengthen my knee."
Keep in mind that "medical advice" is off-topic on Sports SE (and should be elsewhere). As long as it doesn't cross into that territory (eg, I have pain in my knee while exercising for football), these questions would suffice.