Earlswood is good. Being about 3/4 miles south of main town centre, it feels villagey and not so urban, but has easy access to Redhill station for very frequent fast trains, plus it's own station on the mainline too.
Earlswood primary schools plus St John's primary across the A23 coukd he the school you'll get depending on where exactly you live. Use Surrey school website to check using postcodes.
Another nice are is known by Eastate agents as Redgate - near Raffels bridge and between Reigate and Redhill - on the borders. Easy walking distance to station and nice Victorian houses and walking distance to Reigate too. There's a newish primary nearby.
When choosing where to live, look at secondaries too. Some areas of Redhill (like Meadvale) are in Reigate School catchment whisky mots if rEdhill is Warwick which has been more variable. If you're a regular Chruch goers (think at least fortnightly for 3 years for the full Church reference) then you can get into St Bedes which is the most academically successful and has a 6th Form (unlike all the other Reigate state secondaries which feed Reigate College) from anywhere in Redhill, Reugate and surrounding areas...big catchment area for those meeting the religious criteria.
Lots of people like Merstham too - one station up the line towards London and parts like Park 25 walkable to Redhill station. There's a big council estate (quite a bit privately owned but lots still social housing) which feeds Furzefireld Primary, plus the older part of Merstham, - lots of Vuctorian houses which mostly feeds Merstham primary. Again. Like Earkswood, Merstham has a community feel and is both part of Redhill but also its own place. The kids from there are mostly going to the Warwick or in time their nearest is the newly opened Lime Tree secondary, where a primary also opened maybe 4 years ago.
You'll find you can get 3 bed terrace/semi from around £350k in some of the cheaper parts, and pay up to £900k for similar big semis or detached in the more desirable parts.
Then there are the villages to the east like Nutfield, Bletchingley, Godstone, or areas going south like Outwood, Smallfield, Salfords and Reigate and villages to west. They might feed Redhill secondaries but would have own primaries and you'd mostly need a car or decent bike ride to get to Redhill station for the mainline, as their stations tend to be on the branch lines and you'd need to change at Redhill.
Redhill is getting a long drawn out facelift. The cinema and lots of modern flats, plus new shops are being built. The town centre has had several revamps and a big new Sainsbury's. It's not a fancy town but a practical one, having M and S, WH Smiths, Boots etc and a few clothes stores and perhaps less cafes and restuarants than a town of its size might have. It's got quite a mixed population in terms of affluence, with some of Surreys poorest neighbourhoods having RH1 postcodes or being with Reigste and Banstead council....and you see the mix in Redhill town centre,mbut there are relatively few family homes right in the centre and peoole moving to the area tend to go for places like Earlswood, Meadvale, St John's, Mertham, Redgate rather than thebtowncentre, unless buying the new build flats.