MATHS Undergraduate Edinburgh vs Durham vs Bristol

hmm well Bristol has a better reputation then Bath internationally but in the UK their really is not much in it between the two. Cardiff are okay in terms of reputation . Edinburgh have better reputation then Bristol as you know.

it goes
Cambridge
Edinburgh
Bristol
Durham
Bath
Cardiff


However you have missed a few big names off such Imperial College London who are one of the top ten in the world and 13th in the whole world for math.

Warwick who are very strong.

Just wonder which ones are better among these three? This is an international student so international reputation is quite important. Caring most about academic strength but also city & life.
I have applied to Cambridge, Cardiff (Got relative there so much lower expense), Bath and Bristol. I ill withdraw Bristol if other twos are better.
For academic, Edinburgh seems to have the best international reputation as it got a very high ranking in QS for university and its maths course. Whereas Durham has got a better fame in the UK. Generally I don't think I'm really into Bristol but I will stick to it if it is better.
As for city, TBH Edinburgh has got a wonderful outlook as a city but I'm keen on the collegiate life in Durham as well. I'm visiting Bristol so I'll find out the city myself.
Please offer some advice !