Yes, it all depends what your budget is. Didsbury & Chorlton are both great places to live, plenty to do, nice bars, restaurants, etc. Cheetham Hill I would avoid, but that's only because I value my safety and the security of my property and belongings. Some people are different. Why not take a short-term rent somewhere to get the feel for a place before buying? I rented for about 2 years in the Northern Quarter in the city centre about 4 years ago and it was amazing, great bars, right bang in the centre of town, although quite quiet too. Things have really taken off there over the last couple of years so I reckon prices will have rocketed. Good luck, Manchester's a great city to live in.