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This is somethign that can be done, but as pointed out by other posters, you do run the risk that the signal sent to other TVs may have a bit of "ghosting". You can only wathc the one cable channel at a time, so different TVs, would all have to be happy with the same one, or select a terrestrial channel instead.
My setup is indicated in the diagram attached.
Note that if you want to change channels on your STB while watching in another room you would need somethign like a digi eye remote extender. Other threads on this forum discuss those and their compatibility with differing types of Set Top Boxes (not all will work)