You asked about places to stay in Rome and Siena that might be more out of way of the crowds. A factor for Rome is that you don't want to be too far from the sights so that you have to walk too far to get to places, especially with a 4-year-old. That being said, Trastevere (across the river), while it can be touristy, is a pretty area that, on our last trip there, felt more like a neighborhood. Also the Aventine Hill area, though that's on the other side of the Forum, so you might have a distance issue there. In Siena, it's a small-enough city that I think you'll be able to escape the crowds relatively easily. A bigger focus in Siena would be a place where you can easily get to your car, for day trips. I remember previous posters mentioning a hotel outside the walls, but close enough, that might be an option; try doing a search using "Siena."

On the entire tourist-local thing, we have a condo in a tourist destination, but stay there enough to feel kind of like locals. Instead of being annoyed at tourists, or at being one, remind yourself that growing up in Niagara Falls gives you a better perspective, one that allows you to better see things from the locals' point of view.