My bike key is broken off inside the lock
Is it a cable lock like in the image? If so, bolt cutters. You'll be surprised and dismayed to see how easily you can cut a cable lock with a set of bolt cutters (maybe enough to invest in a better quality lock?) They're cheap, easy to find, and will get through most wire cable and some chain (depending on hardness.) They're also the go-to for most bike thieves, so don't be overly conspicuous about using them.