Of course public school kindergarten!

My first-hand experience says so.

Even the kindergarten in private daycare is very good and convenient for you, in the long run the kindergarten in public school is much better:

(1)You son needs to go to public school anyway. Most kids in 1st grade went to the kindergarten in the same school before. By going to public, your son makes friends there first.
(2)Public school has better resources than private daycare. What I meant is private daycare, not a typical private school(starting from grade K). Private school may have good resources but not necessarily private daycare.
(3)Public school will challenge kids based upon their abilities. My kindergartener reads 2nd grade books and learn stuffs based upon abilities in different areas, yet still makes friends with same age kids.

You can find a day-care facility that provides half-day kindergarten facility. Say if your son goes to morning kindergarten in public school, the school bus can drop him at the daycare for lunch and afternoon kindergarten, which finishes at 3:30 or 4pm. You can pay additional hours for daycare (meaning that your son will mainly play after the afternoon kindergarten). (I assume you work full time.) At the end day, you pick up your son from daycare.