schools in Alton are good afaik, has a good 6th Form college. it's a nice enough town. villages outside Alton are lovely.
Other places to consider are Hook (good transport M3 and mailine to Waterloo) housing's probably about the same prices as Fleet/Basing.
it's a large village, but has pubs, a tesco, sainsbury is planned, has takeaways, good primary schools, feeding to good secondary.
there are playgroups, and mums and toddler groups too.
depends what you want, if it's country, peace and quiet, fresh air and green places to run kids legs off, think slight outside of the more towny places.
if commuting is important Hook, hartley wintney are good (HW is more pricey though) Odiham even more so.
Basing is ok...bit of a basingstoke/chineham overspill.
places like Sherfield on Loddon have nice new places to live and you can access train/road system fairly well.
DS does a class in Fleet centre every weekend, so I know the high street well, it has a good range of shops and services. anywhere around here is pretty good for families tbh.