Yes there are tysties (black guillemots) at south stack. Apparently a few pairs breed in Holyhead harbour. They are there all year but go from April to June to see them breeding and in their breeding plumage. In winter they are white with black spots and streaks.
Taking the Puffin Island 'Cruise' out of Beaumaris in July always turns up cracking views of Black Guillemot ( as well as really close views of Puffin ). Phil's directions to the Fish Quay / Outer Harbour lead to the most regular site where the birds are easy to see.