As US passport holders, you can enter Japan for 90 days, provided you have a valid passport. There is no need to apply for a visa in advance.
https://travel.state.gov/content/tra...ree%22%20entry.

If you miss your onward connection at NRT because of a delayed incoming flight, go to the transit desks and have them make alternative arrangements. I expect they will offer accommodation at an airport hotel. There are shuttle buses to the airport hotels. If you prefer to stay a traditional Japanese hotel (a "ryokan"), you would probably need to make your own arrangements. There are a couple in Narita city, which is a short train ride from the airport.