Although a long time ago, I went to Manchester for my undergrad and Sheffield for my masters and while working at Bath I also did some p/t teaching at Bristol.
She really needs to look at the courses in detail first and see if there is one she prefers (although of course optional modules may not always be on offer every year).
If they all seem much of a likeness and there is no clear winner on course, then it is down purely to the type of city she wants to live in. Manchester has huge amounts of stuff going on music/clubs, film and drama wise, but so have Bristol and Sheffield. All are good for getting out into the countryside with excellent hiking groups to either the Pennines or the Breacon Beacons, although Bristol has the advantage for seaside trips to Weston. I think Manchester just about wins out for museums (but then I have a real soft spot for the mummy gallery in the University museum), and the Whitworth Art Gallery is on campus. But then Sheffield has a paternoster in the Arts Tower and the Botanic Gardens are right next to campus. Of the campuses, I think Manchester has the edge, if only for not being at the top of a hill!
Bristol has a quirky, west country, crusty feel to it, almost another country. Mind, Sheffield also has that slight dislocation feel to it, marching to its own rhythm. Manchester is larger than both and I've only really found Londoners who think it is 'small', so if she's not into a big city experience it might not be for her.
Expense-wise, Sheffield is the cheapest for accommodation and certainly when I was there the quality of accommodation was higher for less money than Manchester.
But the course has to come first before making choices of where to live.