There are nice/good value places going for rent around the whitworth - moss side area. Walking distance to the uni, and just out of the way of the madness if you want to keep things tame but with fun still in reach.
Avoid Fallowfield if you want to keep a good arms length with the student chaos, it is pretty much a student town. Generally nice/safe/cheap but known for massive public disturbance and partying, recently with the Police trying to supress it!
There's a general negative vibe linked with the moss side area, however I believe it is more exaggerated/urban myth linked to certain infamous council estates in the area and bad press regarding specific events (not saying crime rates aren't higher overall). However there is much more to it, especially with areas nowhere near the infamous coucil estates/poorer areas, and where you will find the accomodation is very open/safe with a lot of student presence, often placed closer to the uni. Do keep that in mind when doing your research.