There are obviously big privacy concerns/implications with this and you’ll rarely see someone recommend it on Lemmy, but Google’s Location History/Timeline pretty much does exactly what you’re asking. It’s not perfect (for instance if you’re at a shopping center it might record a different store than where you went) but it will keep track of where you went, when you arrived, when you left, and even try to guess how you got there (car, walking, etc.). You can set it to delete this history after a certain number of months.

Another option would be to use a mileage tracker like someone would use to deduct the use of a vehicle on their taxes, such as MileIQ or Everlance. They’ll record when and where you traveled.

If you’re being really paranoid about someone falsely claiming you trashed a place you might also want to consider a Timestamp Camera. This app has a lot of options but not great documentation so you’ll want to play around with its settings. You can have it put street address, latitude/longitude, even a little map overlay directly on the image. Of course, location data and timestamp are automatically baked into the metadata of your pictures by default, but that metadata could be stripped or modified. Someone could claim your timestamps and data baked into the photos were added later or falsified, but these would certainly make a stronger case. I use this app when doing a side gig delivering food and someone selects “hand it to me” but then messages me to just leave it at their door. I’ll take a picture with this app and send it through the delivery app or text message when I drop the food off so they have a record of when and where it was left. I don’t think people have usually tried to scam me or the service, but I’ve read plenty of stories of people trying that and this at least makes it harder to make a false claim.