Manchester is ace, been here over 20 years now, through studentdom and house-ownership.
With the tram/train there's pretty good access into the city from a wide area - but it's a pain going radially around the city (everything goes in and out of the centre, like spokes on a bike)
All directions have areas that are nice and not nice... like everywhere, i guess...
South:
probably most popular (and most well known to any manc students)
Fallowfield, Withington, Didsbury (getting better in that order) are v studenty, with lots of grim rentals.
Sale, Chorlton and Altrincham, Wilmslow, Alderley Edge are quite decent/expensive
avoid Wythenshawe
Stockport is ok, with Heaton Moor and Heaton Chapel being quite desirable (good train link into Manc and close to motorway to drive).
further out, like Knutsford and Mobberly, is getting quite nice, but A6 can be a pain to drive during busy times
South East:
Romily, Marple - v nice and popular - but a pig of a drive during busy times, as limited road options
East:
probably has a worse reputation than it deserves, as long as you go far enough out...
inside the ring-road is pretty iffy unless you want to goto Man City regularly
outside the ring road - avoid Hattersley (and probably Hyde)
but go beyond them to Glossop and it's quite nice, getting into the edge of the Peak District
North East:
Oldham is pretty poor and needs to improve (as does everything between it and the centre), but outside Oldham has some v nice areas.
Saddleworth (Greenfield and Uppermill) are v desirable being on the edge of the Peak district
Moving more northerly there's loads of nice little villages (Delph, Diggle, etc) which are nice, but you'll need to drive to a train/tram to get into the city
North:
Rochdale and Bury are probably the problems, with some bad reputations they may well not deserve (all the time)
Outside Rochdale, Littleborough and Hollingworth are nice
West,
Sadly, I don't know the west as well as I do the East.
inside the M60 - Salford is a mixed bad. Uni there, so quite studenty and some areas of Salford are less-ideal
but Salford Quays has been developed a lot, and is quite nice now.
Can be a pain to get anywhere around there on match days tho, as it's close to Old Trafford/Man U.
M60 West can be a pain around Trafford Park too, especially around Xmas
Outside the M60, I seem to remember thinking some areas of Worsley seemed nice, near the canal
Coming to the city, finding somewhere nice to rent, with some rural greenery and good links to the city - tbh, I'd look Marple (train), Heaton Moor (train), Greenfield (train), Timperley/Sale (tram), Wilmslow (train), Littleborough (train)