Are you going to be renting or buying? What kind of budget do you have?
Avoid west earlham, larkman, mile cross, heartsease, parts of lakenham. I've noticed a lot of properties come up on cadge road/motum road/beecheno road which are places I'd never want to live (and I live quite near there).
Thorpe st Andrew, Sprowston, the 'golden triangle' (priciest area), 'silver triangle' (more up and coming), Costessey are all fine. Slightly further out villages such as stoke holy cross, poringland, bawburgh, easton, rackheath, brundall etc are nice. Plenty I haven't mentioned but it's a start without know what you'd want? Lots of nice schools in the nicer areas.
If budget wasn't a problem for me I'd choose the golden triangle. I used to rent in the area and it's just lovely, good schools, mix of students, professionals and families.