Hello there,
There are quite a lot of other 'moving to Nottingham' threads here, which cover schools and areas in and around the city but perhaps not the surrounding villages so well.
Nottinghamshire villages are quite a contrasting mixture of agricultural - mostly in the south and east of the county - and ex-mining / industrial, more in the north and west, including the Derbyshire border.
The obvious answer to your question is Ruddington. It's a large village, south of Nottingham. Plenty of shops and cafes and a strong local Mums' network (look up Ruddington Mums). Schools are good.
The secondary school at Keyworth seems good, so looking at its catchment might be useful. Keyworth itself is another large village with facilities. Tollerton is nice and the pre-school and primary are considered very good.
For something more rural, the villages around and including Wymeswold and Wysall are lovely, likewise anything in the Vale of Belvoir (pr. Beaver - really).
More suburban, the Beeston - Chilwell - Bramcote - Toton area is nice, an easy commute into Nottingham (tram, train) with lots of good schools. Attenborough has a real village feel, its own train station and is also close, even walkable to Beeston, which is a cafe hub. The river and nature reserve creates a more rural feel.
Hope that's some help 