i live in fallowfield and work in withington, and sometimes i go thru stockport on the a34 when going back home (if the m6 is full of holdups like it was last week) fallowfield is quite nice, but i wouldnt recommend living here if you arent a student as its probably the biggest student area in manchesterand i can pretty much guarantee you wont get a night of uninterupted sleep. withington still has a lot of students but not as many as fallowfield, some nice (and fairly cheap) places to live (if you are renting). didsubury is a bit posher and i rarely go there (just for the pub quiz once a week) but ive heard good things about it.
if you live in fallowfield, withington or didsbury then getting to stockport wont be much of a problem. 15 or 20 minute drive i expect.
if you are looking for places to rent you might want to have a look at
http://www.manchesterstudenthomes.com/forums (its what i used to find my current house) its mostly students (i dont know if you want to live with students or not) but you do find some postgrad and professional houses aswell offering rooms.