To whoever is most organized/willing to keep track of it all. My FI and I live together, and we're planning the wedding together with minimal input from our parents, so we're having ours get mailed back to us, since that just makes the most sense. A friend of mine had them mailed back to her mother's house, because her mother is way more organized. Just do what works best for you, your FI, and your family.
Re: Invitations