Most students live along the Oxford / Wilmslow Road corridor, in areas like Fallowfield, Rusholme and Withington. I've lived in both of the first two areas I've listed, and they were absolutely fine. Others live in areas like Longsight, Levenshulme and Didsbury.
I'd caution against living in Salford Quays - it'd be a pain to get to, and you'd be nowhere near your new friends.
There's a useful map of places that students (well, freshers) tend to frequent here
https://maps.google.co.uk/maps/ms?msid=211506846237564271066.0004d4f6dcbcfcc178f8d&msa=0&ll=53.44142,-2.217522&spn=0.0034,0.009162 One thing to consider is if moving straight in with your bf is the best idea. Few relationships survive the move to uni - everything in your life (and therefore everything that acted as a support to your relationship) changes - where you're living, who you're living with, occupation, job, schedule, membership of any social / sporting organisations and so on. I know only one couple whose relationship survived the move to uni, and they're still together now they've graduated, but the rest all foundered at some point (including one couple who broke up within a week of starting at the same uni...). It should be noted that if you were to break up and were renting a flat together, it would be very difficult to move out before your tenancy is up at the end of the academic year.
So, it may be better to consider living separately in first year, and just seeing quite a lot of each other but also making sure that you expand your social circle beyond each other. If you're still together come second year, that's a good time to move in together (FWIW, the couple I know who are still together didn't live together in first year either).