Hawaiian Airlines links Pago Pago to Honolulu twice a week. Thirty-day advance purchase return fares are cheaper than regular fares, but you must be physically there to buy such a ticket. Don't forget to reconfirm your onward flight if you want to avoid getting bumped.
Inter Island Airways has frequent daily flights to Pago Pago from Apia. Due to currency differences, tickets for the Pago Pago-Apia flight are a third cheaper when purchased in Apia rather than in American Samoa or elsewhere. Most of the Apia flights are on 19-seater aircraft. Beware of baggage handling irregularities on the Apia flights, as damaged, delayed, or lost luggage is routine here—carry anything irreplaceable in your hand luggage.
The Samoa Shipping Corporation's ferry Lady Naomi leaves Pago Pago for Apia once a week. Safety regulations limit the number of passengers aboard to 220, and when that number of tickets has been sold, the ship is "full." Thus it's wise to book before noon a day ahead (take your passport). Ticket sales at the office end at noon on the departure day, after which you must buy your ticket at the wharf and will be the last person to board. The booking agent is Polynesia Shipping, across from the Sadie Thompson Inn. Make sure your name is added to the passenger list or you won't be allowed on board.
Coming from Apia, get a roundtrip ticket if you intend to return as fares are much lower in Samoa. Upon arrival in Pago Pago, you must reconfirm your return ticket at the Polynesia Shipping office. Go aboard early to get a proper berth. The action of the southeast trade winds makes this a smoother trip westbound toward Apia than vice versa (but it can be rough anytime).
Immigration formalities at both ends are chaotic because everyone pushes to be the first person off.
There aren't any scheduled passenger boats from Pago Pago to Tonga, the Cook Islands, or Fiji. The main season for hitching rides to Tonga or Fiji on private yachts is mid-April to October. Somebody at the Pago Pago Yacht Club may be able to advise.