>No David, a Kosher restaurant that follows the kosher laws cannot, and will
>not have any milk or milk products in the establishment.

If it serves meat, that is.  There are lots of kosher dairy restaurants
out there that serve no meat whatsoever.  (Not as helpful for vegetarians
as it sounds, since fish is not considered meat for kashrut purposes.)
It is theoretically possible for a restaurant to serve both milk and
meat dishes if a strict separation is kept, but the logistics make this
very rare.  In any case, in such a kosher restaurant you would always be able
to get reliable and knowledgeable answers about whether things are dairy,
made on dairy equipment, etc. as this is critical information needed to
avoid the prohibited mixing.

--Robyn