I would second most of Copthall's comments, Hampton isn't all A*s and prides itself on keeping all boys for 6th form regardless of their performance at GCSE. It also prides itself on being an old fashioned grammar, it feels like one, and concentrates on traditional boys grammar subjects. It is one of the strongest sporting schools in the country, it has 200 boys a year to pick teams from and they have very successful football and rugby teams at all ages, so the training must be outstanding.
KGS is much smaller and co-ed. You are never going to be able to compete against schools the size of Hampton if you only have a third of the number of their pupils to pick from - this could be frustrating for sporty boys. However, they do very well at hockey and rowing. The sports fields are really good but some distance from the school which is tight for space.
Reeds is a nice school, with really good sports facilities and a strong sporting ethos despite its size. They are usually national tennis champions, and are very strong cricketers. It used to be easy to get in, they have an outstanding SEN department, and boys with dyslexia were sent there. That was a few years ago, it is still generally seen as less desirable than the more selective schools, although I do know a few parents who have taken Reeds instead of Hampton because they think a smaller school will suit their DS better. Its still a bit of a back-up but it is now quite competitive to get into, albeit less than the aforementioned schools. It does give a fair number of bursaries to deprived children, so there is more of a mix of the very poor, very rich and some in the middle.
Radnor never visited, but lots of friends have, they use St Marys sports facilities a 5 minute walk away which are outstanding. They also use other playing fields near the Lensbury (DS's prep plays them there).
As you can probably tell DS is sport mad, these schools may have drama facilities etc, but someone else will have noticed and comment on them. I'm just trying to give you a feel for viewing these schools from a sports mums perspective.
Good Luck with choosing.