The Premier Inn's and Ibis around the city are usually good value. The West Derby Premier Inn's the one I liked, as it was walking distance for me, but I've stayed on the docks, in the centre and over the River in Birkenhead and Greasby, where public transport is easy or you can grab a cab. Saturday won't be cheap, but right now staying at the Premier Inn in Greasby is Fri-Sun £147, Sat-Mon £140 or Sun-Tues £102. Birkenhead and West Derby ain't huge amounts more.
Stuey's right about cab fares, they are ridiculously cheap in Liverpool compared to where I live, but I bussed it or got lifts from strangers going to the game because the locals were just that damn friendly.