Tucked away on the left of the highway (heading away from the bridge) is the Mary MacKillop Chapel, it's Museum, and a lovely indoor/outdoor cafe and shop. It's opposite the site of the old North Sydney Telephone Exchange - now an amazing new building development named (fittingly) 'The Ark'.
There's room inside if the weather is cold or inclement - but the outside area under the trees is my pick. It's a little oasis that you might need on a weekday if you work over this way - and as peaceful as you'd expect.
Here's where you can find it:
Mary MacKillop Place Cafe
7 Mount St