The area around New Alresford is proper rural Hampshire, the sort with more sheep than traffic lights. The town itself is a compact market centre dropped into a ring of small villages and chalk farmland. Green space is never more than a short walk away. Open water, in the shape of the town's pond and the streams feeding it, is close behind. Countryside is the default in every direction, and the town is the exception carved out of it.
On green space, the numbers land close to as good as they come. The average home sits only around 140 metres from its nearest patch of green, which is a two-minute stroll at the outside, and there are something like a dozen separate parks, greens and open spaces within a kilometre of the typical front door. Open water is close as well, roughly 460 metres away on average, and the cycle routes that thread out into the surrounding country pass near the large majority of the town's streets. This is not a place where you have to get in the car to find somewhere to walk the dog.
The character comes from the ring of small settlements around the town as much as from the town itself. Old Alresford sits just to the north across the river, with Bishop's Sutton, Tichborne, Bighton, Abbotstone and Gundleton scattered through the farmland beyond. This is watercress country, and the pond and the old weir on the northern edge hold back a stretch of water that has been part of the local map since the medieval town was first laid out. History sits thick on the ground out here. The scheduled monuments in the area include the medieval Alresford Bridge and the deserted village of Abbotstone, a whole settlement that quietly emptied out and never came back, which is the kind of thing you find when you go looking in this part of Hampshire. The built-up town is tight and walkable, and the moment you leave it you are straight into open country. The shops and services cluster in the centre, while the villages are places to live rather than places to buy your groceries.
On the surroundings, this is as strong as the scorecard gets, a clean five out of five. New Alresford hands you a walkable town wrapped in green space and quiet Hampshire villages, with water and open farmland a few minutes away in any direction. If the landscape you actually live in matters to you, the area around the town is the easiest thing about the place to recommend.