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Stockton Heath is useful for shops and restaurants, though I actually think that Culcheth has a better range of shops and you get more for your money price wise with the housing stock. Stockton Heath has a good stock of houses of different styles. (What's your budget? This will affect the advice I would give).
Appleton is unofficially split into old and new areas. It starts south of the London bridge pub (on the corner of dingleway) but the area around the London bridge is a bit mixed (our friends moved away from that area due to people relieving themselves in the front garden on the way home). That said, south way and greenway are very nice.
Old appleton includes the area around windmill lane but that's very expensive. If you look around the golf club, so that's fairways, beech ways, pine way etc you will find a 1970s estate with good sized houses and pretty big gardens often ripe for redevelopment if you fancy a project that will add value. There is a good co-op here with a doctors and a pharmacy.
Further south you will find newer housing estates around beamish close, Hatfield gardens, stone acre gardens and stone hill gardens. These are just examples - there are lots of different Roads. The older the house, the bigger the garden. Houses on beamish close were some of the last to be built (1995?) so have smaller plots and are correspondingly cheaper. The three storey houses on pewterspear are on very small plots with slippery pavements!
The newer areas of appleton are served very well for open space, sports pitches etc. very pleasant place to be.
Grappenhall is a large area. The village itself is the area around the church (church lane/broad lane/bell house lane). This is a really nice little community with a thriving community centre, nice little walks, a cricket club and a sports club. The areas around st Wilfred's drive are good solid family areas of 1930 s semi detached houses. Kids play in the street on scooters. For detached, there's Sharon park close but that does suffer a bit from traffic noise as its close to a fast moving stretch of the A50 (though handy for the M6).
There are old Victorian houses around Alexandra road and balmoral road, near the Bridgwater canal. Lovely stock of houses around the £500k mark but tend to have small gardens. I general, the area of grappenhall the other side of the A50 is less desirable - so that's the north side of knutsford road between the A50 and the ship canal. Nothing wrong with it per se, just not as desirable and prices reflect that.
Grappenhall heys is a more recent development of larger houses, though there are some three storey terraces. It's not my cup of tea (quite isolated) but it has a little walled garden which is a sort of local charity who are trying to raise money to improve facilities and I think to restore a greenhouse. From grappenhall heys you can walk downhill to grappenhall village, though this is an isolated dog walkers type of path rather than somewhere you might feel comfortable to walk routinely (I walked it alone last week and didn't enjoy it).
Latchford is much more diverse. There is a very large council estate along with a lot of terraced housing and some semis but that said, it has a great range of shops. Restaurants there aren't great.
Have a look also at Stretton.
Schools - there are no bad ones really. Church schools in grappenhall (st wilfreds) and stretton (st matthews) are small, friendly community schools and well regarded. Grappenhall heys school, cobbs infants in appleton all good. Bradshaw lane a bit more mixed I think, but I don't hear bad things. Stockton Heath has st thomas' and Stockton Heath primary. The latter was in special measures, which I think was a bit unfair actually.