I went to Newcastle University and I am from Surrey, so I can give you some insights into these two, but no nothing of Glasgow I'm afraid.
Newcastle is a great city, its compact, so easy to get around, and has a good selection of shops, bars, clubs, galleries, museums and a surprising amount of quirky cafes and independent restaurants. There is quite a variety of accommodation for first years, I stayed in Leazes but wouldn't recommend it (for various reasons), I had friends who stayed in Windsor Terrace though and quite enjoyed it. In second and third year most people live in Jesmond, a good area, I always felt safe and its quite leafy and green, with parks, shops, gyms, bars and restaurants - and all about a 30 min walk from the main city centre (or a 10 min train journey). There is plenty of accommodation too, so you don't need to worry about finding a place. In regards to getting a job, as far as I'm aware most of my friends who wanted one, managed to get one, its a city after all, so there are plenty of opportunities and quite a few that are especially catered to students. The weather can be pretty cold, but at least it's on the east coast of England, which means it gets less rain than cities on the west coast (supposedly); but no one goes to Newcastle for its good weather. I did Geography, so can't speak for the Psychology department, but generally always got on with my tutors and lecturers well and heard similar stories from other students. Living costs in Newcastle are also pretty cheap, especially in regards to nights out, taxis and restaurants; although there was a rumour that apparently the Tesco in Jesmond is the most expensive in the country, but I never noticed it particularly in relation to the one back home in Surrey.
I would never recommend going to university in Surrey for your undergraduate degree, but I guess as I grew up in the county so have quite a distorted view of it. I should note, I don't live in Guildford, but do go there for shopping/clubbing/visiting friends. The weather is decent and it's a beautiful county, I've been privileged to group up here, but its just not that exciting and pretty expensive. Also if you were planning to settle in the UK, you might very well end up getting a job in London, thus could end up in Surrey anyway at a later point in your life.
TL;DR: Newcastle is much more exciting and cheap than Surrey, but the weather is worse.