OK, Royal Grammar School (RGS) in High Wycombe is likely the most famous RGS in England, but it's far from being the only one. According to the almighty wikipedia, there are 7 RGS in England. I believe RGS, High Wycombe boasts Benjamin Disraeli as one of its former pupils, and probably many other things.
So, enough of that and let's talk about Royal Grammar School Newcastle Upon Tyne which I'll just call RGS, for short!
RGS was founded somewhere between 1525 and 1545. Yeah, that's a pretty big gap. If I've read its history correctly, the merchant, Thomas Horsley let money in his will, in 1525, for the founding of a school and the school was in operation by 1545. If they had the 5 hundred year celebration in 2025 I'd have a pretty good chance of seeing it and being there, 2045 is a different matter! I'm not even sure of its original name, once Queen Elizabeth gave it its royal charter it became known as the Royal Grammar School.
The school has moved a number of times since its founding and has been at its present site for somewhat more than 100 years (but almost certainly less than 200). If I were motivated, I'd go find a web page on it and give more precise dates. It was, for at least 450 years, an all-boys school only becoming co-educational relatively recently. The school had varying numbers of students but, toward the latter part of the 20th century the number was approximately 850 in the senior school (ages 11-18) and some number (100 or so) in the junior school.
Back in the early 1920s, a former pupil and benefactor Sir Arthur Sutherland gave money to the school to build changing rooms for sports activities as well as a swimming pool (which was also used by other nearby schools as well as Newcastle University students at various times of the week).
Academic standards were high with an entrance exam to get into the school, emphasis on academic excellence, and most pupils going on to University.
Unlike most of the surrounding schools, the main fall/winter sport was rugby which meant that inter-school competitions were fewer than at many of the other schools in the area. I'd guess that the big rugby event of the year was the game with Ampleforth! After athletics in spring, the summer sport was, you've guessed it, cricket.
It's really hard to describe a school like RGS in a few words; it's a school with a long history, famous former pupils (known as old novos), and many traditions. Maybe the best analogy would be Hogwarts without the magic! Pretty much everything else is accurate, though!
One tradition I'll mention is that it used to be the case (changes in the election cycle in the early 1970s altered this) that the first duty of the elected Lord Mayor of Newcastle would be to visit the school, give a speech, and ask the headmaster to give the pupils a half-day's holiday!. In earlier times, the pupils used to carry the Lord Mayor, sitting in a chair on a heavy table, around the city walls. There was a rumor that this all came to a disastrous end around the time when there were only 7 students in the school and a very fat mayor!
The wikipedia article is pretty good if you want to know more.