I understand your worry about your daughter being alone in an unfamiliar city for the first time.
There are two main exits from Piccadilly railway station. One is next to the taxi rank on Fairfield St (at the junction of Fairfield St and London Rd, near a Costa and cash machine on Google maps) and the other is kind of up a side road/spur called Station Approach which runs from street level up to the station alongside London Road, which is a busy road.
I've just looked on Google maps. On Streetview, it looks like there's an entrance to the hotel on London Rd not far from the Fairfield St/London Rd entrance (?).
To get to the Oxford Rd campus of MMU, there are many, many, many buses from Piccadilly Gardens (I think 42,142,43,143 as well as several others, she can ask a bus driver there tomorrow. I'm sure they'll help). There are also regularly trains between Manchester Piccadilly and Manchester Oxford Rd stations, although the university is a walk or bus ride from the station.
From Manchester Oxford Rd station, which the buses mentioned above will pass) your daughter, should walk down the approach road (down the hill to the junction), turn right onto Oxford Rd so that Sainsburys and the Palace Theatre are both on her left, cross the main road (Oxford Rd) to the bus stops on the other side and then get the bus south away from the city centre towards the universities). She could also walk down the same road to the university. It's one straight road to where the Oxford Rd buildings are.
If she's going to the newish campus in Hulme, she will need to check which bus goes there (I think one is a Trafford Centre bus, but I'm not sure). It's potentially walkable but several blocks further so probably easier to get a bus or taxi the first time.
Google maps is usually pretty good at planning a route worth public transport.