It depends what you mean by "fantastic". Unfortunately, you won't find anything in Cornwall to rival top schools elsewhere in the country, especially London. You do need to be realistic about what is available.
I would suggest you move either somewhere near Truro, or somewhere where your child could reasonable commute to Plymouth if you want a real choice about the school your children go to. These areas also give the best options/choice when it comes to a lot of post-16 education.
IME most towns have one or two state secondaries, with very mixed catchments. Some of these schools are taking a lot more pupils than the number they were origionally built for, but most still have nice grounds, outside space etc. A lot of high achievers will go elsewhere for sixth-form, normally to Truro or to Plymouth, sometimes with very long commutes. Do be aware that most roads and public transport in Cornwall is quite slow, so this will lengthen your commute.
If you want something really "fantastic", I would say you would need to go private. Truro school is probably one of the schools with the best reputation, although there are of course other private schools available. There are no Grammar schools within Cornwall, but some children from SE Cornwall do go to the Grammar schools in Plymouth. There are also various private options available in Plymouth and the surrounding area.
As a final point, whilst there are lots of plusses to living in Cornwall, do be aware that in a lot of the small towns etc there are major drugs problems, and most teenagers will be exposed to drugs. I'm sure it's no different to any rural area of the country, but as there is very little else to do, this can be a major problem.
I hope this helps a bit.