What part of Warrington is WA1?
WA1 is just outside of town centre (lived there for nigh on 20 years, WA2 before that), it's very convenient, I wouldn't say desirable as such but it's not horrible by any means. As you say the better parts are on the outskirts, Stockton Heath, Appleton, Lymm, Grappenhall etc.
As a town though Warrington is a bit grim.