Hi,
As Jonny says, night time would be best. The harbour is actually much shallower than it looks. There is a bar at the mouth, which is where most pier anglers mistakenly target. At low water, the depth there is no more than 3 feet. Tides are typically between 4 to 5 metres, so a high tide adds significantly to that depth, and at night fish other than fabs and flounder might feel brave enough to enter. If it has rained heavily, there will be too much fresh water coming down the river though, so you want a dry period if possible.
Going back to the depth, the deepest part is actually really close in, adjacent to the wall where the fishing boats tie up, and even at low tide there is 9-10 feet there. There are a few obstructions, I guess junk from the boats, but you'd be very unlucky if you got snagged. If there are no fishing boats there at the time, that's where I would go. The boat channel continues seawards very close in until just after the steps and where the wooden pier starts. It then heads diagonally across the harbour to the Warkworth side.
Unless you are really restricted, or have mobility issue and need to fish out of your car, there are plenty of better alternatives, as Jonny points out. The Seafood centre has a small selection of tackle for sale, and they have frozen baits and even fresh ragworm.
I keep a boat at the marina. She's out the water currently having some work done, but I'm hoping to be back in by mid October, so if you see Bellini pass, give us a wave.
Enjoy your stay. It's a great place to visit whatever, and if you do bag a decent fish, do let us know.