And if you're bona fide praying Catholic, there is Notre Dame, feeders are the Catholic primary schools.
Notre Dame I think topped the exam league tables last year. It's not private, and is of course now obliged to take a few non-catholics.
If it interests you, results league tables here: www.telegraph.co.uk/education/2016/05/05/compare-your-school-primary-gcse-and-a-level-results/
Hunters Bar is another very diverse school, lots going on - juniors head is leaving at the end of this year, but the teaching staff are excellent, so I don't think it'll be a problem. Catchment is parts of Eccy Road, Nether Edge.
There is currently a sort of "dual" system of entry to secondary schools, both your postcode, and the feeder schools. There is in the South West of the city a sort of doubling up available to you, such that Tapton and King Edwards catchments cross over, High Storrs and Silverdale. King Ecgberts (Jessica Ennis is an alumni there) is away out in Totley Dore, so sort of stands alone. When there was more curricula freedom these pairs had a more distinctive niche - so Silverdale styled itself as the "academic" school, high storrs had some drama, sports art type distinction. But I think that's been eroded somewhat - and High Storrs outperformed Silverdale last year at A level.
There is a shortage of secondary school places available in the south west and north east of the city, see www.sheffield.gov.uk/education/about-us/consultation/school-places.html
and there is intent to build another secondary school - when first proposed was intended to be up and running (academy of course) by 2018. But the council plans were really rather stupid, having ringfenced the two better sites for housing, and suggesting putting the school on the current Holt House infants site, and shuffling around a load of junior places, I think it has gone back to consultation. The two better sites are the Bannerdale centre site off the Abbeydale road, and hilariously, the Abbeydale Grange school site - this school was mothballed about 6 years ago........................... There is a really really interesting old article about this particular part of sheffield and the schools here www.theguardian.com/uk/1999/sep/15/nickdavies
If you are interested in social geography, Danny Dorling has been Professor at Sheffield (now at Oxford) and wrote a lot about the local area. He describes the social gradient across the city as being steeper than that across Johannesburg - the south west corner being very affluent.