Google Owens Park, mate. That's where i would feel ok if my daughter was going to uni in Mcr.
You have the main Rd (Wilmslow Rd) with a bus literally every minute into the centre of Manchester passing the Uni. A Bus in the other direction will take her right to wythenshawe hospital. A busy night life around Fallowfield if that's her thing and a huge park (Platt Fields) although i don't think any park is a safe place for a lone woman these days unfortunately . Your daughter may be better joining the Aquatics centre near the uni initially until she meets some jogging partners. Fallowfield, Ladybarn, Withington and Didsbury (depends on budget) are the best and busiest student areas, best wishes.