For larger organizations, https://www.charitynavigator.org/ is great for this purpose. They don't handle local orgs, but it's still valuable.
I also think it might be good not to be too critical in general. As in, I don't care too much about overhead for most of my purchases, so if an organisation delivers a good amount of Good, then I'm not going to worry too much about whether it's the absolute most they can do. It's not like I donate that significant a part of my income anyway.
It's exactly the same for charity giving. (Perhaps more so for me, since my contributions cut into my living expenses in a noticeable way.)