I don't know if I can help or not, andisa. And I am just a lowly PhD student who teaches, so I am both naive and inexperienced (though I do care).
I'd say for a start, you don't want to choose the university before you choose the course. A place may be brilliant for 90% of its courses, but terribly for the other 10 - or, it could be wonderful but just wrong for your DC, who needs a different kind of wonderful. Take for example medicine at Oxbridge - it is very good, but if you are keen to be a hands-on medic, you might actually get impatient and prefer somewhere less research-oriented.
But, assuming you want to know how good a specific course at a specic university is, you can look at published league tables by subject. You can also look at things like the average grades the university asks for - by and large, the higher these are, the more comeptitive and the better it is. And you can look at how many students drop out every year (IMO very important), and how many get jobs in a year.
The above will give you a bit of an idea of how well-respected and competitive the course is. You do then really need to know if it will suit your child. There are big differences in terms of teaching/assessment methods.
For example, some places will assess students through all three years, so each year some of your work counts to the final grade. Other places, the only thing that determines the grade is a few concentrated hours of exams in the final year. You need to know what suits you as a student. You'll be much more likely to get a high grade if you are in a place that teaches teh way you want.
Content can also vary a lot - you need to check what will be studied. For example, if you do English Lit and go to Cambridge, you can avoid the twentieth century and literary theory almost completely; at Leeds, you will need to understand both.
If you can find a course that is reasonably well-respected, and suits you in terms of content and teaching style, that is what you want. I hope that helps but sorry if not!