Anyone who has ever been a local knows that locals spend time living their life; they rarely go to museums, etc in their own town; and if they do they probably go to specific ones multiple times (the ones that go with their hobbies, say).

There is something to "not being a stereotypical tourist" but that's easy enough to do by being polite, and paying attention to what is going on, and wandering off the beaten path now and then.

Visiting off-season can be a great deal, especially if you're not concerned with weather (for example, if you're going to be visiting museums in Rome, they will be open during the rain as well as the shine).