What is Ray Bradbury's tone towards the rocket men in The Illustrated Man?

Tone, of course, is an author's attitude towards his or her subject.  I am intrigued by your question because more than one of the stories within The Illustrated Man collection by Ray Bradbury concerns the "rocket men" you mention in your question.  In reality, though, that doesn't matter because Ray Bradbury's tone toward any of "the rocket men" you ask about is always the same:  it is a tone of both disillusionment and disagreement.

There are three stories in question all of which contain the aforementioned "rocket men":  "The Rocket," "The Rocket Man," and "Kaleidoscope."  In the former story, a guy wastes his savings in order to simply pretend or "simulate" a real rocket trip because he can't pay for a real one.  The author, Ray Bradbury, reveals his tone indirectly through the happenings of the story.  In "The Rocket Man" a husband leaves his wife and family time and time again in order to go back to the alluring "drug" of the stars.  Humanity is left behind for the romantic ideal of starlit space.  Again, Bradbury shows his own thoughts indirectly by showing that no good comes from this husband's space travel.  The latter story, "Kaleidoscope," all of the "rocket men" here are thrown tragically into space (to certain death) when their spaceship explodes.  Here, Bradbury reveals his thoughts in the character of Hollis who realizes that the illusion of dreams can't constitute a memory of reality.  One of the best quotes that sums up the tone is about the mother in one of the stories who is steeped in reality (as opposed to the "dreams" of the "rocket men"):

Mother wasn't afraid of the sky in the day so much, but it was the night stars that she wanted to turn off, and sometimes I could almost see her reaching for a switch in her mind, but never finding it.

In conclusion, it's important to note that no matter which story you are referring to, Bradbury's tone remains the same:  one of disagreement or disillusionment towards the "rocket men" and their space travel.  This leads to a further idea that the simpler the life is, the better for the human race.

What is the tone or mood of "The City" in Ray Bradbury's "The Illustrated Man"?

Tone refers to the way the author feels about the subject of the text, and mood refers to the emotional atmosphere created by the text itself and is more akin to how the reader is meant to feel. The mood of this story is foreboding and menacing. Early on, the reader learns that the city is alive, that it has "waited" for a long time, twenty thousand years to be exact, until, one day, a rocket appears in the sky.

When men emerge from the ship, the city listens to their speech, watches them from windows, smells their feet and clothes and even eyeballs, weighs them, and eventually snatches their captain, emptying him of his human life and filling him up with organs made by the city of metal. Ultimately, once all the men have been killed by the city, and given new life as the city, they plan to return to Earth with "golden bombs of disease culture" in the rocket they came in. This does not bode well for Earth or the people still living on it.

The tone of the story is more understated, though. Bradbury does not seem to condone the city's actions, nor does he explicitly condemn them. He is rather matter-of-fact in allowing the men to be callously disemboweled by the city. The city claims, via the captain's body, that it "was to be a balancing machine, a litmus, an antenna to test all future space travelers," to learn if they were the descendants of the "Earthmen" who left the city's inhabitants "to die of a terrible disease, a form of leprosy with no cure."

If this is true, then it seems that turnabout is fair play. If people abuse other people, abandon them in their time of need, or exploit them somehow, then they ought to expect consequences. Those consequences are meted out, here, and Bradbury seems to look on with a sense that those consequences were predictable and perhaps even just.