2-3 a year! Crumbs...
We saw two - right next door to one another. In our town, all Yr5 children spend a whole school day at each of these two schools - they go as a whole class with their teacher and have a great time.
Then there are open days at the schools for parents of Yr5 children, followed by open evenings in the September they are in Yr 6, i.e. a few weeks before application forms have to be in.
I would say Yr 5 is a good time rather than Yr 2, schools can change so much over a 4 year period, you really want a more up to date view of the schools. Also, most of the open days/evenings and activities there are geared more towards Yr 5/6 children.
As a family, we didn't actually let our children choose, although we listened to their views. For one thing, we wanted one school for all 3 children, so we had to do the choosing for no.1 otherwise the other 2 would have thought it unfair.
Also, from what we could see of other children allowed to choose, they couldn't see any wider picture but made their decisions on really trivial grounds (liking the school dinners, liking the look of the P.E. changing rooms...) or on the basis of where their friends might go. Since both our elder two have made new friends and more or less left all their old friends behind within a few weeks of starting secondary school this didn't seem wise!
Between now and Yr 5, I would try to narrow your list to a maximum of 3-5 real possibles, then take it from there. You'll go mad otherwise!