Perhaps surprisingly, lots of them.  In the United States, leaders
include
the National Zoological Garden in Washington, D.C., the San Diego Zoo,
Steinhart Aquarium in San Francisco, the Denver Zoo's Tropical Discovery
exhibit, Zoo Atlanta, and many more (contributions solicited).  The
Baltimore
Zoo gets extra brownie points for having many snakes in the children's
zoo.

A number of zoos in Europe have outstanding herp collections, often
equipped
with great naturalistic settings; the Rotterdam Zoo is a world leader,
and
the author wishes to take this opportunity to plug the zoo in Frankfurt
as
well.

At least three zoos in the US have tuataras.  The St. Louis Zoo has some
that
are said to be off-exhibit at this writing, and the Dallas and Toledo
Zoos 
have recently opened exhibits. The London Zoo is now reported to have a
pair 
of tuataras on display; the only other exhibit that I know of outside 
New Zealand.

More information for this question is always welcome.

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Section 6: Obtaining and identifying herps