There's a good anchorage in Village Bay, sheltered from the prevailing S Westerlies but it's well open to the East.
The western side is rather steep to, if I remember correctly, so not much shelter in an easterly but you can always go to Barra.
Mingulay is a fabulous island, but not the easiest of places to visit.
Village Bay is the only tenable anchorage, and even then it's very subject to swell, especially towards high water. As a result, the anchorage can be very rolly.
Landing can be difficult, too, as the beach shelves quite steeply, and there is usually a dump at the surfline, making it difficult (even dangerous) to land on the beach. Generally it is easier to land on the rocks to the North or South of the beach, where there are gullies that a dinghy can be driven into. Even then it can be quite a scramble getting people in and out, especially those of a nervous disposition!
I am told that the anchorage off the old slip on the North side of Berneray is better swell wise, although it's hard to see why.
There are good reasons why Mingulay was evacuated, mostly relating to the above problems!