This is a common question for someone who is moving into the area.
South of the river I would go for Wilford, West Bridgford, Radcliffe on Trent etc. The outlying villages are also nice but obviously travelling time if you commute to the city is then a factor. Gotham, Bunny, Keyworth are all worth a look.
On the other side of town, Arnold, Mapperley and parts of Carlton are nice. Burton Joyce is pleasant but again you are moving away from Nottingham and travelling time increases.
House prices are cheaper in Derbyshire and the commute is very doable depending on where you choose. Breaston, Borrowash, Risley and Draycott are close to both the A52 and the M1.
To the North of the county, Ravenshead is very pleasant but perhaps a bit too far from the ‘bright lights’ of town.
Please get in touch if you need any more help deciding.