Those out-of-town people who need him to personally deliver the invitations are just these ones. Invitations for everyone else can be sent by courier; you just need to check the time and call to chat for a bit. As for the local people in New York, it's much simpler; they're basically colleagues and friends, so the invitations can be delivered on the way.
Jimmy went around several places consecutively and felt quite exhausted. Because he carries a weapon with him, every time he goes to the airport he needs to register and complete procedures, which are far more complicated than normal boarding procedures and require at least an hour of waiting time. These rules are overly cumbersome, and they've only been this troublesome since 9/11—before that, it was much simpler.
Returning to New York, Jimmy dropped off his luggage at home. Nia wasn't in the apartment; he figured she was either back home or out shopping or doing spa activities. Jimmy didn't call her; he just went out to the bar.
