All the student accommodation in the cities you mention OP will be reasonably priced. These cities have enormous student populations and several universities with residential students. The cities you mention are large and geared up to students but with lots of other things to do. The universities are all Russell Group so no differentiation there however, there may be differences in the content of the courses offered, the A levels required to get a place (although unlikley any will be the highest offers), and in the league tables for the subject so look at those factors.
All cities have levels of crime and some of it is robberies of student accommodation. Therefore if a student is living in private rented accommodation, make sure windows and doors are secure. Don't leave expensive laptops on show etc. Regretably murders can happen anywhere! There was a notable one in Bristol in the student area. That is the MOST expensive area of Bristol where houses sell for in excess of £2m. Students there do not necessarily live in the "cheaper" areas. In fact, not at all!
Most students actually like where they decide to go to university. If you spend some time in the favoured cities you tend to get a feeling of what it is like to live there. Oxbridge, Bristol, Durham and St Andrews have a high number of privately educated young people. Sheffield is significantly lower down in this particular league table. The city is politically Labour and feels like it. I am a regular visitor. Bristol has a pretty inactive students' union. Most students do not bother with it. Sheffield used to have a very vibrant students' union and it is a good value city. However, all the others you mention are hardly expensive either.
I would check out what matters to the student: course and learning facilites , good value accommodation, weather (?), student union activities, delis and tea shops, new or traditional halls of residence, reputation of university, distance from home, staying in a certain location (North, Scotland, South Coast etc), sports facilities, clubs and pubs, job prospects - they are all in the mix for some people. Everyone will have a different opinion!