Lovely places to live in the city: Wollaton, Mapperley, The Park
Lovely places to live in the surrounding area: West Bridgford, Any of the villages in Rushcliffe - I'd recommend Keyworth, Radcliffe on Trent and Bingham for facilities and schools.
Gedling village, Burton Joyce, Lowdham, Gunthorpe all lovely but harder to get to QMC.
Avoid: Bilborough, St Anns, Broxtowe, Sneinton, Aspley.
I've lived here all my life (mainly in Rushcliffe, but also Wollaton) and it has great shopping, facilities, good transport links, schools and countryside in all the areas I have listed worth living in. Inner city estates have previously had a bit of a reputation, but this is in no way relfect of the area as a whole.
The M1 and A1 run up either side of the county giving you great links to the rest of the country and the Midland Mainline runs straight through. East Midlands Airport is very close by too.
QMC is an amazing hospital - they saved my life last year and their staff continue to give me great care. The staff have been amazing.