Bath uni for maths?

Hi, I’m applying for maths and I was originally planning on applying to:
Cambridge, Warwick, Durham, York and Nottingham - I have been to open days for all of them except Warwick and I really liked the unis, but I did do work experience at Warwick (for physics not maths) and I remember quite liking the campus. But recently I was also thinking about applying to bath - also haven’t been on the open day, as it’s pretty good and it seems like a really pretty city. I’m not sure whether I should maybe replace Warwick with Bath, or maybe replace Nottingham or York but that would only leave me with one ‘backup/insurance’ if I don’t get into Cambridge. I really like the city of York and the uni, but I did prefer the maths department at Nottingham as they were just really nice, but equally if I’m living there for three years maybe the city is more important? but If anyone has any advice on what they think might be the best option that would be great.

Hi, I’m applying for maths and I was originally planning on applying to:
Cambridge, Warwick, Durham, York and Nottingham - I have been to open days for all of them except Warwick and I really liked the unis, but I did do work experience at Warwick (for physics not maths) and I remember quite liking the campus. But recently I was also thinking about applying to bath - also haven’t been on the open day, as it’s pretty good and it seems like a really pretty city. I’m not sure whether I should maybe replace Warwick with Bath, or maybe replace Nottingham or York but that would only leave me with one ‘backup/insurance’ if I don’t get into Cambridge. I really like the city of York and the uni, but I did prefer the maths department at Nottingham as they were just really nice, but equally if I’m living there for three years maybe the city is more important? but If anyone has any advice on what they think might be the best option that would be great.