I am also from 'down south' - born in London and grew up in Herts, then London again, went to university in a southern city. I now live in Manchester.
It's a brilliant city - especially for students. It has one of the largest student populations in Europe, which they're incredibly well catered for. It's lively with great night life, but in a way that means there's something for everyone - there are plenty of places for low-key socialising so it's not like it's all big clubs etc. There are lots of small, quirky indie/artsy venues as well as clubs and a big creative scene with lots of opportunities to see live music in every conceivable niche genre and so on. The arts/culture and creative scene in general is really great and there are also endless opportunities for sports and so on. And similar to the night life, there's a huge variety of shopping and so on - obviously all the big high street chains, trendy places and designer shops are here, but loads of really good independent niche/quirky shops as well.
I'd very much say it's a city with something for everyone - it has a reputation as a party city but to be honest it's way more varied than that. I wasn't a party animal as a student, but I would have loved to be a student here! And if your DD is more of an outdoorsy type, it's very close indeed to moorlands, the Peaks and the Pennines and I'm sure the university will have clubs for walking/climbing etc.
Public transport is very good and now cheaper than most other big cities.
Crime is no worse than in any other big city. I've lived here for over 20 years now and have never been a victim of crime at all - and that included when I lived in a very gritty city centre area.
I always feel that it rains a lot but statistically, there is no significant difference in rainfall between here and the south. And we've had the same hot, dry summer that everyone else has had.