I'm British, and grew up just north of Bristol.
Since I was 18, I've lived in:
- Exeter: 4 years (3 years for university (between 2001 and 2005), 6 months for work (2010/11), 3 months for work (2012), 3 months for work (2015))
- with my parents just north of Bristol (on and off between 2001 and 2010)
- Bristol (1 year, 2008/09)
- Shropshire: 4 months (2011)
- Lincoln: last 5 years (2011-2016)
Personally, my favourite place to live has been Bristol (I'm dying to get back there, but I can't due to no work locations nearby). After that, I would say Exeter, which is where my company headquarters are located, so chances are, I'll end up back there in the future.
Exeter is a lovely city - not too big, but it has all the amenities you need (unlike Lincoln, where I live right now). It's only 1.5 hours from Bristol, the schools are good, it has one of the top universities in the country, plus several other good universities within a couple of hours' drive and it's a pretty safe place to live.
Bath is nice as well, though I find it a bit cramped and touristy, plus it's expensive to live in... actually the southwest in general is pretty expensive. I recently bought a 3-bed semi in Lincoln for about half the price it would cost me in Bristol, Bath or Exeter.
I don't know Brighton at all, and although my mum grew up in Edinburgh, I've never really been there. However, as you said, Edinburgh is cheaper and you have the benefit of free Scottish universities (and NHS prescriptions). Plus, we don't know what will happen with Brexit and/or Scottish independence in the future.