Eastleigh is well stocked with schools, from infant classes right up to a sixth-form college. Primaries sit in most corners of the town. There is a secondary that serves the bulk of local families. There is a college good enough to have once taught Colin Firth. Plenty of choice, then, with the familiar catch that choice and getting a place are two very different things.
At primary level the town spreads its options around rather than funnelling everyone to one gate. Cherbourg Primary School, Norwood Primary and Pre-School, Nightingale Primary School and The Crescent Primary School cover different parts of the town, and the Shakespeare Infant School and Shakespeare Junior School split the youngest years the traditional way, with infants handed on to juniors a few years later. It is a decent geographic spread, which matters more than parents expect until they are standing at the school gate working out the walk.
For older children, Crestwood Community School is the main secondary serving the town, and once the exams are done Barton Peveril Sixth Form College is the local step up to A-levels and the reason a few Eastleigh teenagers end up sharing an alumni list with a future Oscar winner. Between them they carry most of the town's secondary and post-sixteen load.
Now the honest part. This page does not carry the inspection grades that would let you rank these schools one against another, so treat the list as a map of what exists rather than a league table with a winner at the top. Naming a school here is not the same as recommending it, and it is certainly not a promise. If the grades matter to you, and for most buyers they should, look them up for the specific schools before you fall for a specific house.
The other thing worth saying plainly is that living near a school does not get your child into it. Hampshire allocates places by its own rules, and proximity is one factor among several rather than a guaranteed ticket. Every year a batch of families discover in the spring that the house they bought for the school did not quite reach the school, and the ones who read the admissions criteria first tend not to be in that batch. Buy the house because you want the house. Treat the nearest school as a hope you have checked, not a right you have purchased.
So what are the schools like in Eastleigh. Numerous, spread sensibly across the town, and covering every stage a family needs without anyone having to drive to the next borough. Without grades to separate the strong from the ordinary, average is the fair verdict, and average with this many options within walking distance is a long way from a problem.