Depends if you want genuinely in Shoreditch or just walking distance. London City Travelodge was only built a few years ago and is decent (make sure it's that exact one not the Tower Hill / Liverpool Street etc ones as they are a lot worse).
Ibis have one that is allegedly Shoreditch (technically Whitechapel) and quite nice, I used to get advance rooms there for £40 but it's a lot more expensive now. Then they have a genuine budget Ibis hotel labelled as Whitechapel, which is much worse but fairly cheap.