One of my favourite places in the City is St. Patrick's, Church Hill - right near Wynard.
It is a gorgeous church inside, with a handy little shrine to the Virigin.
Outside is a nice little garden grotto for praying in, but best of all is a small cafe in an old chapel that serves tea and sandwiches, and is surely the City's best kept secret! I love going there, and it is the perfect place to meet friends (though conversation should be kept to gentle levels - most of the other tables are occupied by elderly Catholic ladies discreetly dozing off).
I was there just the other day, meeting a dear old friend for lunch.