Your best city for music, out of the whole list - is Sheffield. I've done every city in GB (including Northern Ireland), except Londonderry.
OK - I haven't partied in all of them, but I've done the night life in every one on your list (What.... No Manchester or Liverpool??!!) Sheffield is the clear winner, with Newcastle (a fairly close) second.
Never assume that because London is so big, that it's music scene is the best. It's an OK place for theatre and live shows - but it's way down the list for quality nightclubs and live bands. And yes, you're so right - it's (extremely) expensive.
Good luck with your venture.