The best place is where it is most functional. In front of the sink, where you have it, is often the most useful to catch splashing water.

I keep my anti fatigue mat under my sink area.

If you do one at all, I'd pick one that is the width of the drawers below the sink.

IMO rugs in kitchens are just tripping hazards and honestly it is easier to wipe up a spill than wash arug all the time . You have what appears to be vinyl floor why a rug at all?