Another option for ticketing to consider is to purchase two separate tickets. When searching online for ROC (Rochester, NY) – HND/NRT (Tokyo, JP) with stop over somewhere along the way, then it is possible that the search results will contain only fares which allow stop over along the way.
Fares which allow stop over along the way, not transit at connecting airport (in old paper ticketing fares allow stop over were indicated by “O” in front of city listed on the ticket, and when fare rule does not allow stop over were indicated by “X” in front of city listed on the ticket), can be higher than simple transit connection only.
Which means if you are planning ROC-HNL-HND/NRT, rather than try to purchase one ROC-HND/NRT round trip ticket which allows stop over at HNL, buying two separate tickets ROC-HNL round trip and HNL-HND/NRT round trip.
Disadvantage of purchasing two separate tickets:
• These days some airlines are implementing the rule that baggage will not be checked through to the final destinations when purchased as two separate tickets. Which means if you have two separate round trip ticket, ROC-HNL and HNL-HND/NRT then airline at ROC may not check your baggage all the way to Tokyo.
However, in your situation you are planning few days of stop over so likely you are planning to collect your luggage at stop over airport. Then this should not be a problem.
• When having two separate tickets, strictly from fare rule airlines will not be responsible for missing the connecting flight due to flight delay or flight cancellation.
Again, in your case you are planning to spend a day or two at a stop over point, so having first flight delayed or cancelled should not cause major problem in your trip plan.
All these many make things more complicated, but you simply have to compare fares and determine which route and single ticket or two separate tickets, which stop over city is least expensive, the day of the week, etc.