There's a number of places you could move to but I guess it all depends on your budget. There are some really nice apartments around Salford Quays due to the BBC moving there and the rengeneration that is happening within that area. Other places you might like to try are Withington or Didsbury. They're a little out of the city centre but are generally very nice areas to live plus they are also situated on a main bus route which runs throughout the day and night taking you right into the centre.

There's also Fallowfield which is known as being mostly astudent area. It's not as nice as the places above but obviously if you're a student too then it'd probably be worth looking at.