[X] You need to talk to somebody about this.
-[X] Takako might know somebody appropriate.
This is a pretty big deal, and it would be nice to know what exactly the ramifications of it are. Take is probably the best candidate for knowing what it might mean, legally speaking, believing us about it, and not squealing to the authorities. Plus "I'm secretly a member of a noble family" is the sort of thing that's directly relevant to her interests, and she might take Ichigo hiding that poorly.
Talking to someone in 10th division is tough, because we don't know any of them, or even whether they've were around when Isshin was captain. Walking up, knocking on the door, and saying "hey, I'm possibly the son of your MIA former captain" is tricky.
It would be nice to hook up with the fireworks and booze side of the family. I bet they'd be receptive to another clan member who has some power and is on track to be a shinigami. They might give Ichigo a hard time about it, but if they believed him, they'd be happy to hear that Isshin's alive, and happy to have more cousins. And unlikely to tell the authorities about anything. Plus another link to the Yoruichi faction.