This might sound counter intuitive but you might try cycling for a while.

This will strengthen the quads but without the shock/road impact. If you can find a way of securing your feet to the pedals (clip-ons), then you will have a regular stroke with both feet moving in parallel which should be beneficial as well.

I have moved from cycling to running this year and found that despite my strong quads, an old knee injury led me to collapse my right ankle inwards. From this I developed shin splints, calf and achilles problems! I now run with a foot/ankle support and a knee support and - did I mention Dr Foots Sports inserts?

In summary, you have to isolate the cause which may not be where you feel the most pain!

Good luck