I work at a university. It's rural and not a household name.
Most of the students seem to have brightly coloured hair, piercings, tattoos, alternative dress etc. A massive proportion of the students on my course define themselves as anything but straight. There's all sorts of relationships, gay, poly, fluid, asexual, demisexual, "throuples". We have lots of trans and non binary students.
The last time I was a student was 7 years ago. I was the only female student on my course who had never had a sexual encounter with a woman, only one without tattoos etc.
Being LGBT inclusive, as far as I am aware, is just a very very normal part of university. Students will face a disciplinary if there are any hints of discrimination, bullying, hateful ideology towards LGBT staff or students.
Alternative dress has always been part of the student life. All the way back to Beatniks in the 50s.
Any major city should be fine. Universities with a strong Arts or Liberal Studies background will be especially welcoming. Maybe pick a city with a big LGBT scene already and apply there. Manchester springs to mind, it's where most of my LGBT friends have lived for at least some part of their lives and has a few educational establishments.