he was looking for the key to open kingdom hearts, obviously*
but yeah, like ragerunner said, he wanted the key to arthur's house so he could... i dunno, kick sue out of the village or something? lecture her for being rude? he locks her up after egg corridor to trade for toroko, but i wonder what he was originally planning to do before she was kidnapped, i don't think any of the mimiga were aware the doctor was specifically looking for sue before then.
thinking about it, if jack knew there was a key at arthur's grave, why didn't he just tell king or check himself [thinking emoji]
*note, i don't know enough about kingdom hearts to know if this is funny