We're in Richmond and there are lots of schools, especially if you don't mind commuting/paying! The first thing to be aware of is that for state schools (except Tiffin, see below), whether you get in is based on how near the school you live. For private schools, it's whether you pass the entrance exam and can pay! (But obviously for both, they have to have a place free).
State (free) schools:
Teddington and Orleans Park are probably the best, closely followed by Greycourt and Christ's (but you have to be CofE or live very close to that one). My state pick, if i was moving to the Richmond area but could choose where I lived, would be to buy somewhere near to Teddington School, which has just been rebuilt and is meant to be fab. (but property doesn't come cheap around there). Tiffin is a state school, but it is what's known as a "grammar" - it is highly selective academically, I can't over-estimate how hard it is to get in to (1 in 10 who apply get in, but if you have a very bright child, maybe worth calling them - I wouldn't imagine they have many places for late entry though).
Private (fee-paying) schools:
Kingston Grammar and Hampton are pretty near (fairly academic but worth a try), then there are lots of slightly less academic ones going into Surrey, but if you don't mind a commute, they're definitely worth a look - Halliford, St James' (Ashford), Reed's and I think there are lots more. The Good Schools Guide (a book or I think online) will point you in the right direction. I suppose if you're looking for somewhere very academic, you could commute into London to Latymer, St Paul's, Westminster...out of my league!
Hope that helps!