Liverpool is one of the most cosmopolitan cities in UK, is well used to visitors, is a happy city with two magnificent Cathedrals linked by Hope Street, has the oldest Chinatown in Europe, the biggest Chinese Arch outside of China, a night-life unmatched by any of the other cities you mention, and a very large student population catered for by the many attractions and events in the city, and is cheaper to stay in than Bristol or Manchester. Far from being isolated, it has good transport connections to the whole of UK, including a fast train service to London (2 1/2 hours), excellent bus and long-distance coach connections, and a modern airport serving many domestic and European destinations. It is officially the 5th safest city in UK. Manchester is much less safe, being 21st on the list, and is easily visited from Liverpool by frequent buses and trains since it is only 30 miles away. It is a regular and busy commuter route.
Liverpool life
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Birmingham is more central, is cheap to stay in, very cosmolitan, and has some excellent attractions, including a large and busy international airport, is a major hub for National Express coaches, has three excellent railway stations, and a totally re-built city centre, the best concert hall acoustics in UK in the Birmingham Symphony Hall,and a great arts Festival.
Both cities offer a great variety of entertainment, history, surrounding countryside and historic towns, and either of them would make an excellent base for exploring Britain and for studying.
Bristol is a beautiful city and is in a beautiful area, but the West Country is more prone to severe weather and to flooding than the other places you mention. Students at Bristol have a history of militancy, and student troubles have been quite severe in the past. Much quieter now, but students are not as well liked by the city's general population because of the past troubles.
At one time Bristol was Britain's leading port, a role later taken by Liverpool.
It is the most expensive of the four places for living in, but has some scenic compensations for it.
The West Country has easy access from Birmingham, with many of the historic towns like Bath and Wells, north and east of Bristol, and famous beauty spots like Symmon's Yat being easily visited from both cities..
http://www.wyenot.com/yatrock.htm ..
Birmingham, however,unlike Bristol, is far from the sea, so if coastlines are a favoured landscape, Bristol will suit you well.
The glorious coast of Somerset and easy access to South Wales and the rugged and beautiful Pembrokeshire coast make it a winner for landscapes.
Liverpool has good and fast access to the Lake District, and Birmingham has Cannock Chase nearby as well as the good services to the West Country, both particularly favoured by walkers and cyclists for the good scenery they offer.
Manchester's nearest large scenic attraction is the Peak District just south and east of the city, which is a rival to the Lake District for fell walking and for beautiful scenery, though it's lakes are the three Derwent Reservoirs, the largest being the lovely Ladybower Reservoir.
http://www.kayukay.co.uk/ladybowerreserv…
To be honest, any of the four cities could give you a great stay in England and offer you easy travel to scenic and historic areas as well as fast and frequent transport into London. Cheapest is Birmingham, then Liverpool, Manchester, and lastly Bristol.
For racial harmony, Liverpool wins easily, then Birmingham, Manchester, and lastly again is Bristol.
The west of England in general is sadly, like some of the more conservative areas of the south, like Chichester, not as friendly as the north. The most cosmopolitan city in the south of England, apart from London, is Brighton, on the south coast. I have family nearby, and in other parts of southern England.I am a southerner now living in the north, so I am not being unfairly biased.
I know both north and south , and visit all over the UK frequently.
However, how you do is also a matter of your own input into where you live.
Many people of other cultures live happily in the west, including in Bristol. Some are not happy in Liverpool, though by far the majority are very happy to have chosen it as a place to study, and likewise with Birmingham. Those two would be top of my list, with Manchester trailing well behind in third place, and sadly the lovely Bristol in fourth place despite it's attractions, because of the higher cost of living and lower expectations of social happiness, but everyone is different. My brother lived in Bristol for a while, and enjoyed it, but moved back to the equally lovely Chilterns where we come from.
Best of luck and enjoy where you live.