What schools care about demonstrated interest?

The problem with knowing which colleges care about demonstrated interest is that the colleges basically have to tell us for us as counselors to know. That list is about as comprehensive as anything you're going to find on the internet.

As a rule of thumb though, you can look at it like this—is it a college that has difficulty filling its classes each year? I.e., does it have a low yield? If that's not a number you can find, check how many waitlist acceptances it offers in a given year, because a lot of waitlist acceptances typically means a low yield (while low waitlist acceptances mean a high yield). Colleges with low yield are a lot likelier to care about demonstrated interest.

And if you can't find anything about a particular school, it's better to be safe than sorry—demonstrated interest is never going to hurt you as long as you're not badgering its admissions officers or counselors with questions. Signing up for a virtual tour or sending a couple of questions to the admissions office shouldn't take up a ridiculous amount of your time.