В Париже для меня слишком жарко! Нет уж, лучше Женева, там прохладнее!
I wonder if "нет уж" serves to emphasise the comparative "лучше" in some way? How is this expression usually used?
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Yes, you're right, "нет уж" expression serves as an intensifier, introducing a (somewhat) emotional attitude of the speaker into the phrase, sometimes even as a joke. It does not add anything to the core meaning of the phrase.
Think of its meaning as of: "oh no(, you don't); no way you'd get me/him/her/us/... (agreeing to smth., doing smth., etc.); me no fool".