Does anyone have any suggestions for quiet public spaces in sheffield city center where I could sit and meditate? I was thinking the Cathedral?

I think the Cathedral is probably your best best (or the Catholic St Mary's). I don't really know of anywhere else city centre wise. You could try the Botanical gardens or one of the parks just outside the city centre (Endcliffe perhaps)?

It depends exactly what you're looking for, meditation covers quite a wide sphere, but if you just want quiet and relaxing then the Cathedral should be fine.