Visited Leeds with daughter on open day, and she studies physics at Lancaster. All of them are good unis. Lancaster city is a smaller city compared with the other two cities. Manchester being the biggest. Theres still plenty to do there with the castle, williamson park, morecambe, the lakes, and she catches the train to manchester as well. Lots of bars, 3 clubs. She likes pub quizzing and also goes to the herbarium cafe for board games night on occasion. She also does the badminton on a sunday at the Lancasters sport centre, and was part of the disney society in first year. there are lots of societies there. She is an undergrad, but she has a lot of postgrad friends, some who live in the same flat in private company halls in the city (penny street). You can live on campus as well. Lancaster has 9 colleges, but if its just masters for a year or so, you will probably be in graduate college. Each college has its own bar as well. Lots of eateries on campus, and a couple of mini market shops for essentials. Theres main supermarkets in the city. City is 15 mins away on a bus, and if living in the city, its worth having a 'stagecoach' bus pass, not so much if you live on campus as you might not travel as frequently. Library is enormous, one of the biggest ive seen on the open days. With it being finance you will likely to be in the swanky 'LUMS' Lancaster uni management school, which is really new. I know they do quantative finance there.
Lancaster uni itself is big as well with a lake and a woodland walk which goes around the uni for 2 miles. If you want a city thats not so big and overwhelming, but has all you need still, then Lancaster is the place for you.