As someone from Leeds, I can vouch for the fact that the social scene here is excellent and you won’t find that you’re struggling to find different things to do!
Manchester is also an amazing city, it’s absolutely huge (the city centre and university area is bigger than Leeds) and there are loads of bars and stuff.
Having visited all three universities, I personally found the universities of Manchester and Birmingham to be huge and felt like I’d feel quite anonymous there, but that’s just my opinion - they are both very good universities so congratulations on getting offers from them.
I find that Leeds is not only a great university (it won university of the year last year) but it is also a really nice city with loads to do.