"Kahit saan" is a better answer when someone asks you 'where'. For example:
"Saan mo gusto kumain?" (Where do you want to eat?)
"Kahit saan!" (Anywhere!)
*answering "Saan man" using the same question would be very weird, and the one you're talking to would joke you about being very "malalim" (sublime) /using of non-colloquial words in an inappropriate situation.
Where "saan man" is more frequently used to start a sentence or a thought, mainly used for formal writing. It is usually followed by something, like what's gonna happen if you go "saan man".
"Saan man tayo magpunta, kung kasama kita, ayos na ang lahat." (Wherever we'll go, if I'm with you, everything is okay.)
"Mabubuhay ako, saan mo man ako dalhin." / "Saan mo man ako dalhin, mabubuhay ako." ("I can live wherever you will take me.")
*unlike "kahit saan", you can use it without requisites.