It would be more helpful if you could say what course your DD is applying to.
My DD is arty and quirky, and studying a STEM degree. She has never been one of the "cool girls", nor has she wanted to be, but she has found her tribe at university.
If your DD wants to avoid the "rahs" then the following universities have over a third of students coming from private schools: Bristol, Durham, Exeter, and Edinburgh, plus Oxbridge. (Rah is a term coined by the state school students about the privately educated, and I believe this term is used at every university)
Also, Russell Group, universities don't necessarily offer the best courses. You really need to look at the best university for the course rather than a high ranking RG university. Bath, Lancaster and Loughborough are not part of the Russell Group, but are more highly regarded than most RG universities.
Manchester is most definitely not a campus university. DD looked at it twice and declared that she just didn't like Manchester as it is too big (we live rurally).
DD is at Newcastle and loves the city. It has a party reputation, but partying is optional. DD isn't a party girl and still has a great social life.