It is personal preference - but I like it at the very bottom. Something farther up to match works - as well.

Where ever you like it to be.

On long pants I like to embroider from about 2"-3" above the hem up along the seam and matching smaller embroidery on the pockets. On pedal pushers I think that about 1 1/2 inches above the hem would look pretty, up the seam or around the entire leg.
On the pocket looks pretty but more trouble if the garment is already made; on the hip looks smart, too, or on a yoke across the back just below the beltline.
I'm not too keen on embroideries on the knees or the backside, i.e. the seat of the pants, especially for anyone older than a small child.
AlmaG.

If you can print out a template of your design you can place it around and see what looks the best.

Not actually an answer, but I just wanted to say I love the term 'pedal pushers'. Haven't heard it since the early 1960's.

I've used the term "pedal pushers" and had a few weird looks until I explained they used to be called that when I was a kid, but now when they brought them around again they now call them capri pants.
As some said it really is personal preference, but do up a template as mentioned and place it until you figure its right (in your opinion, of course).
Good luck!

Pedal pushers, clam diggers, calf huggers, culottes, crop pants and capris, they all look good with embroidery no matter where you put it.

No rule of thumb, put where it is most pleasing to you..good luck ripping a part etc.

Have not heard the word 'Pedal Pusher' in many years.