As mother to another prospective K, I am in your shoes. I would find the lack of response from the public school troubling (I Bet the privates called you right back!

That said, you do need to tour before making the decision - I was pleasantly surprised by the "feel"of the school.
There shouldn't be a process for visiting the school though. Find out who the school counselor is (most schools seem to have decent web pages) and call her directly. If that doesnt work, just show up. Even if they can't show you around right then, you'll at least get a response.
Good luck!