Hi ginajacques. Whereabouts will you be living in Tunbridge Wells as that will probably dictate partly where your DS goes to school? Do you want a Catholic school *that's easy - there is only one!) or don't you mind. Is your DH working in Tunbridge Wells or commuting to elsewhere? A lot of people here commute to London by train so live around Tunbridge Wells station (in the area called the Village which is pretty expensive) or High Brooms station (which is ok). Car can be a pain as there are only 2 main roads in and out of town (A21, A26) and they get rammed resulting in people using a lot of the back roads to cut through.
Catchment for schools varies from one year to the next (the only school to list the roads that are in catchment is St James'). School places have been tight here for the past few years so the council added extra classes to some schools for a few years but some have now gone back to 1 or 2 form entry as they do not have the site space to continue at 2 or 3 form entry. You will probably be looking at getting him into any school then moving him nearer to where you live once a place comes up.
The 2 best schools here at the moment with outstanding OFSTEDs are Claremont Primary and Bishops Down Primary. Neither of these are affiliated to any particular religion. Both of these are in very expensive parts of town (Claremont in the Village area near Tunbridge Wells station where a 3 bed house can cost anything from £400k) and Bishops Down in the Culverden area of town. Both have had several years of doubling their reception intake but Bishops Down is now back to 1 form entry (30 places) and this year 24 are already taken by siblings. Claremont I think is taking 60 but again at least half are taken by siblings this year. I've heard better things about Bishops Down than Claremont.
There is only one Catholic primary which is St Augustine's in the St John's area of town. The only things I know about it are that 10% of their curriculum time is spent on religious education and they have a new head this year. To apply there you have to fill out a form signed by your priest (called a SIF form) as well as the normal application form as they prioritise Catholics over distance from school.
Otherwise you have St John's C E , St James' C E, St Barnabas C E, St Peters C E, Southborough, Broadwater Down and St Mark's C E. Both St Matthew's at High Brooms and Temple Grove Academy in Sherwood are in special measures so you may want to avoid them! There is also a free school called The Wells. It only opened in September this year so I don't really know what people think of it yet.
Application is through the County as clam says not the schools directly. details here. Primary school offers are being made on 15th April so the schools won't be able to tell you anything at the moment other than to book you in for a visit. I'd contact the County council and ask for their advice. There should be a list of all the schools here on the their website and there is a booklet for you to read to apply booklet here.
Sorry that's a bit of an essay
but hope it helps. PM if you want - I've lived here for a while now and my DS is going to school in Sept so have just been through the process myself!