I think Sherwood, Mapperley or potentially West Bridgford for a young couple. Sherwood is my favourite, it has a nice community feels, lots going on and is a bit bohemian. West Bridgford is a bit more pricy and very yummy mummy, some people like that but others are not so keen.
There's also lots of other areas that are pleasant enough to live in, but are maybe a bit dreary. Like Wollaton, Long Eaton,Wilford, Arnold, Carlton.
Personally I live in one of the places that people have said to avoid, but I love it for it's accessibility to the centre, transport links, diversity and Asian supermarkets. Plus the fact you get a lot more house for your money. We've never had any problems either.
It depends what you are looking for. For example Sneinton is a mixture between hipsters and multi ethnic inner city community. It isn't the quietest place or the most crime free, but some people love it.