I have anchored in both hunter and mud bay, both are pretty protected in a south wind with good holding. Hunter is more scenic, but if the wind is predicted to shift to the north with much force mud bay is bigger and you can anchor tucked up against the NW side for more protection and a longer distance to the south shore in case you drag. For some reason every time we end up in either one the weather goes bad.
An option is catch a park buoy at spencer spit, it is very exposed to wind but the spit acts like a breakwater so if you chose the leeward side the water is flat, there are buoys on both sides and the beach is great. Passing between the spit and Frost island is a sphincter tightening experience, but it works.
Another very protected option for your first night is blind bay, it is pretty protected from all directions but especially from the south. If you do go read the guide book carefully about the entrance near blind island, rocks are not your friends.
just writing this makes me jealous, we will not be up there until late July. Have fun and report back often.