CARES has what I think you think you're asking for under aircraft services/aircraft records. Neither an aircraft nor airman registry search will tell you where an airplane is based or operated, only the address the registration holder/pilot provided, if not blocked by the registrant. My airplane has, on occasion, been based >1000mi from the address on the registration (which was unblocked at the time) and on my pilot certs (blocked before I owned an airplane).
Personally, I'm glad the FAA is at least making some progress, however small, in blocking release of PII. If that means someone will pass over my airplane if or when it comes up for sale, it's a sacrifice I'm willing to make.
Nauga,
under a rock
[/flying. even the airport it's probably based at.
If we are talking single engine piston aircraft the owners address especially if it's someone's name usually tells you where the plane is based except for corporate names with a Delaware address.
You can back that up with ADSB information that usually shows where it's been flying even where it is based at.