You'd have a "good shot" at all of them with AAAAB at AS anyway, depending on what you're predicted for A2 of course.
They're all good unis anyway. Going by the the Good University Guide league tables:
Warwick: 8th overall, joint 2nd for A&F (with Edinburgh)
Nottingham: 14th overall, 4th for A&F
Edinburgh: 16th overall, joint 2nd for A&F (with Warwick)
As for the places, they all have their ups and downs: Edinburgh's a really nice city in all aspects, but it's not very central to the rest of the UK since it's in Scotland. Warwick's a nice place but it's quite small and Coventry isn't the most exciting city in the world. Nottingham's a lot more lively than the other two but it's not the safest city in the world.
Myself, I'd choose Edinburgh, but that's neither here nor there what I'd choose.