`var` is entirely syntactic sugar (compile-time type inference) and there's no runtime cost associated with it.
I find it makes most (but not all) code more readable, particularly given that we have great IDEs/tooling in the .NET world.
I agree, by using var you need to name your variable better therefore making your code more readable. Rather than relying on the interface/class definition to explain to someone why you used "obj".
To var or not to var is purely a "tabs 'n' spaces" debate, but doesn't affect performance.
It will affect the performance of someone trying to read your code.