Hmm, I'm concerned that you're asking us because of some mistaken impression that our opinions actually matter....go wherever you feel most comfortable and where you think you'll be happy - thats the most important thing! (I mean, seriously, haven't you read enough posts on here from people from Oxbridge that show life their isn't all peachy).
But since you ask, those are definitely some high quality establishments you've chosen in terms of how they're regarded...
LSE - the London unis are pretty much regarded to come above Russel group universities, by virtue of being in London (I dont mean all London unis, just LSE, KCL and UCL). Of these, LSE is definitely the top, educating probably around as many foriegn prime ministers as Oxbridge, give or take. It is extremely well looked upon, and if you don't come from London, London will blow your mind.
Warwick - a very well regarded Philosophy course which a friend of mine seems to love and all the people on it are very friendly. Be aware that its campus contained though, and tiny.
Edinburgh - Again, one of the best regarded universities after Oxbridge. Very difficult to get into actually, they ask for high grades, but the city itself is wicked.
Nottingham - for many arts subject has higher application ratios than Oxbridge (i,e 11 people to a place) but is a great student town and very well respected.
All the above is merely subjective and you should probably ignore it and go and visit some unis for yourself.
PS - Leeds is wicked! (And no, I dont come from there, it was my second choice and I loved it).