At the present time, there are a few (still living) people who represent the physics community in the eyes of the English-speaking public. The most popular are probably the following (in no particular order):
There wasn’t a particular order, but Neil Degrasse Tyson, for me, is definitely #1. This is partly because of his central role in the remake of the popular educational series Cosmos: A Spacetime Odyssey With Neil deGrasse Tyson Revealed. The other traits that make him stand out among the others are: (a) he is a gifted, articulate public speaker, (b) he engages with comedians, pop stars, etc. on his podcast Star Talk in good humor unlike any other physicist can, and (c) he is not (or at least less) biased toward one particular subfield of physics. These traits are also shared by Bill Nye, though I would argue that Tyson is a more eloquent orator.
Michio Kaku is almost disingenuous in his attempts to draw in the public, marketing lofty ideas without concrete scientific backing. My criticisms of Brian Greene, Sean Carroll and Stephen Hawking, is that they are scientists first, and public engagement is a side-project to them. Of course this is in no way a true criticism, but when it comes to representing a field in the eyes of the public, I believe that Tyson has it won because he is willing to engage with others in topics outside his field of study. In his podcast, Tyson even goes so far as to talk about the origins of salt as well as the art of how to make a good wine.
More bluntly put, Neil Degrasse Tyson represents the different facets of physics much better than any high-energy or string theorist could, because they have nothing to say about my particular field of study, condensed matter physics (which incidentally is the largest subfield of physics). Tyson does not sell to the public any unverified theories (including string theory), but just sticks to what we know to be the best theories in describing the physical world. I would like to see him speak more about superconductivity, superfluidity and Bose-Einstein condensation every once in a while, but no one is perfect! Jokes aside, I am proud to have Tyson representing our field in the eyes of the public, and I hope that he keeps the baton for many years to come.