Liverpool - 25 minutes west, easily accessed by either bus or train, which will both take you into the city centre without having to transfer
Chester - 30 minutes south, by public transport you need to get a bus into Runcorn - Halton Lea shopping centre, where you then transfer onto another bus into Chester
Manchester - 40 minutes east, both widnes and hough green train stations run regularly into Manchester. There's also the option of going by bus via Warrington, though that may take 3 or more transfers to do so.
