I'm reasonably familiar with Kimberley and have mixed feelings about it, not sure I would make a particular point of relocating there, although it does have a few things going for it in terms of amenities, transport, countryside and property prices - and as others have said, neighbouring Watnall and Nuthall are worth a look. School-wise though, although Kimberley is not the worst (gets better exam ratings etc than alternatives in Eastwood, Hucknall, Selston for example) you can still do better elsewhere in the county.
Not that familiar with Mapperley although we did consider it ourselves some years ago and it felt a bit hemmed in... depends what your preference is, but we're happier being not too urban.
Beeston seems good from a multicultural point of view, not sure about primaries but I think part of Beeston is within catchment for the Alderman White school in Bramcote which I is OK I think. But as others have said West Bridgford and nearby Rushcliffe secondaries have the best reputation around Nottingham by quite a long chalk (no pun intended, seeing as they don't have blackboards these days :)).
There's also Wollaton, which seems to be regarded as a nice area for the most part (home to Wollaton Hall and deer park) - schools include Bluecoat Wollaton Academy and Fernwood School.
Outside the city itself, if schools are a priority (again, I can only really comment on secondary) then it may also be worth a look at Bingham (Toot Hill School), Burton Joyce (Carlton le Willows Academy) and Radcliffe-on-Trent (South Notts Academy).
Some useful pages to research if you haven't already:
www.nottinghamshire.gov.uk/education/school-admissions/school-catchment-areas
www.compare-school-performance.service.gov.uk/
parentview.ofsted.gov.uk/
Good luck in your endeavours!